then count the Perpendicular 50 â… on one Leg and half the distance between the Rafter-feet or half breadth of the Frame at that place on the other Leg and the Parallel distance between shall be the true Length of the Rafter required Then for the Hips Length first make AM and BM equal to AE or BE at one end and make CN and DN equal to DF or CF and draw the Lines MM and NN at both ends also make Ab and Bb equal to AB and Ca and Da equal to CD and draw the Diagonal Lines AS and BS and CO and DO at each end extended and set down the measures of them These Lines being drawn you have the half Diagonal Lines AS and BS and CO and DO and may measure them by your Scale to find their Lengths or set the Rule to the Angles AES and BES find them by the 30 Scale also you have the bevel-Bevel-ends of the Frame and the nearest distance over from side to side of the Frame Then for the Hips Length and Angles thus Set the 30 Scales square and count the Perpendicular Height LG on one Leg 50 â… and each half Diagonal Line c. one after another on the other Leg and the Parallel distance between shall be the true Length of the several Hips required Example The Parallel distance between 5 Foot-o-Inches â… the common Perpendicular counted on one 30 Scale and 8 Foot 1 Inch the longest Diagonal Line AS counted on the other 30 Scale shall give 9 Foot 6 Inches for the Length of one Hip AP laterally And the Parallel distance between 5 0-â… the common perpendicular and 6 Foot 6 Inches the other Diagonal Line BS shall give the lateral measure of 8 Foot 3 Inches the length of BP the other Hip-Rafter for the broadest end of the Frame AB Again the Parallel distance between 5 0-â… the common Perpendicular and 6 Foot 4 Inches the great Diagonal Line CO at the narrowest end shall give 8 Foot 1 Inch for the Hip-Rafter CP And the Parallel distance between 5 0-â… the Perpendicular and 5 Foot-0-Inch-0-the lesser Diagonal Line DO shall give 7 Foot 2 Inches for the Hips length DP to stand over the Diagonal Line DO Note also that if to the Compass points standing parallelly you lay a Rule and to the Rule so laid and the 30 Scales at each end a Bevel and set it according to the Rule and 30 Scales it shall give the true Angle of the Hips at the Raising-piece and King-post which 8 Angles in these 4 Hips are exprest by the Lines and Letters in the Scheme thus PAS and PBS PDO and PCO the 4 Angles at the Raising-piece And SPA and SPB OPC and OPD the 4 Angles at the King-post Whose length you may prove by Mr. Pope's excellent way making SP and OP equal to LG on the extended Diagonal Line and drawing the Lines AP BP CP DP for the 4 Hip-Rafters length required Or for more proof thus also by the Rule as before in Square Roofs Set the 30 Scales Square and take the Parallel Extent from 7 Foot 2-¾ the Rafters length at the broader end on one 30 Scale to 6 Foot 2 Inches more then ½ the Bevel-end by 1 Foot the half quantity of Bevelling and it shall give 9 Foot 6 Inches for the Hip AP and from 7-2-¾ to 4-2 one Foot less than the half Bevel-end to 8 Foot ¼ the Hip BP Also the Par. extent from 6 Foot 5-½ the Rafters Length at the lesser end to 5 Foot 0-¾ one Foot more than 4-0-¾ the half little Bevel-end shall give 8 1-½ for the Hip PC And the Extent from 6-5-4 8 the Rafters length to 3-0-¾ 1 Foot less than the half Bevel-end gives 7-1-½ the Hip DP as before Note That by the working these 3 ways you may be sure to prevent any mistakes that may happen in working one way only Lastly For the Angles on the outside or backs of the Hips Take every several Hips Length laterally between your Compasses and set one Point in the Length of the Bevel-end or rather in a mean between AB the Bevel-end and MM at the greater end or CD and NN at the lesser end and open or shut the 30 Scales till the other Point falls on the Hips Length that you work for then for the longer Hip count more and for the shorter Hip less by half the Inches Bevelling then the whole breadth over at the end and take the Parallel nearest distance from thence to the 30 Scale for a nearest distance which nearest distance you must keep Then take the whole Diagonal Line Perpendicular to the Hip wrought for viz. the shortest Diagonal Line for the longest Hip at each end between your Compasses and make it a Parallel in the nearest distance last found and then the 30 Scales are set to the Angle of the back of the Hip required Example in this Figure for the longest Hip. Take 9 Foot 6 Inches the Hips Length AP between your Compasses and set one point in 10 Foot one Inch a mean between AB 10 Foot 4 and MM 9-10 ½ and open or shut the Rule till the other point stands in 9 Foot 6 the Hips length first taken Then the nearest distance from 9 Foot 4 Inches one Foot less than 10 f. 4 Inch. the bevel-Bevel-end distance over to the other 30 Scale shall give 7 10 a nearest distance from the point b to AP the Hip raised over AS the Diagonal Then the Lateral Extent Bb of the whole Diagonal Line 12 f. 7 Inch. being made a parallel in 7 10 the nearest distance last found shall set the 30 Scales to the Angle at R the back of the Hip required measured by taking Parallel 30 and measuring at laterally on the Chords it is about 108 Degrees Secondly Take 8 f. 4 Inches the other Hips Length between your Compasses and setting 1 point in 10 f. 1 Inch as before open or shut the Rule till the other point falls in 8 4 the Hips Length Then the nearest distance from 11 Foot 4 Inches 1 Foot more than 10 Foot 4 Inches the distance of the bevel-Bevel-end to the Common Line of the other 30 Scale shall be when measured Laterally from the Center 9 Foot fere for a nearest distance Then 15 Foot 8 Inches the longer Diagonal Line being made a Parallel in 9 Foot fere the nearest distance last found sets the 30 Scales to 121 Degrees the Angle required the back of the shorter Hip required The same work serves for the other end being near the same Angles Which you may prove by M. Will. Pope's excellent way thus find the middle between S and A or S and B at Q then the nearest distance from Q to BP or AP near lay to R and draw the Lines RE RM for the Angles at R the back of the Hips required Moreover if you raise 4 Perpendiculars cutting the Points O and S the two places of the King-posts being perpendicular to the Raising-pieces AC end BD as the
4 prick-Prick-lines ♉ S â™ S ♌ O and ♊ O do shew and lay the length of each Hip from his proper corner ABCD as AP from A to ♈ and â™ BP from B to ♈ and ♉ DP from D to ♊ and ♋ CP from C to ♌ and ♋ then draw lines from point to point as in the Figure Then ♠♌ and ♉ ♊ are the two Ridges when turned right over OS and C ♋ D is the least Hip and A ♈ B is the greater Hip as Mr. Pope hath well shewed Thus much for Hipt Roofs Use XVII To find the Length and Angles of every Principal particular Rafter in Frames broader at one end than the other The Perpendicular as before was hinted is to be the same all over the Roof Therefore open the Rule Square and take from the Perpendicular on one Leg to the half breadth of the Frame on the other Leg measure it from the Center and that is the Length required For the Angles lay a Rule to the Compass-points and set a Bevel as before is shewed and you have the Angles at the Raising-piece and Ridge of the House to cut the Rafters feet by The same Rule serves to draw out a pair of Well-Stairs to give Hypothenusaes or strings at any particular height and breadth for the 30 Scales set Square and the Perpendicular height counted on one Leg and the breadth on the other Leg the measure between is always the Hypothenusa or string in flying Stairs as may plainly appear Use XVIII To find the Length and Angles of Collar-Beams in any Roof Take the whole breadth of the Frame between your Compasses and set one point in the Length of the Rafter on one Leg and the other point in the same place on the ether Leg then the two Legs represent the two Principal Rafters and a Rule laid to the Compass-points represents the Raising-piece then at any height that you please above the Raising-piece apply a Rule parallel to it and the measure between laid from the Center gives the length remembring to add wood for the Tenons and a Bevel laid to the 30 Scale and Rule gives the true Angle to cut it by where the Timbers be square Use XIX To find the Lengths and Angles of Rafters and Purloyns in Bevel Frames The Length of the Rafters is shewed before to find it by the half breadth of the Square or Bevel-end and the Perpendicular answerable to that Roof as afterwards in the Example And the Angle of the Foot and outsides or backs of the Bevel-end Rafters and the upright of the Gable end must be to an Angle less and more than 90 degrees by the Angle at the corner of the Frame where that Rafter is to stand being more at the sharp Angle and less at the blunt Angle as in Figure IV you may see the true quantity of which Angle is thus found by the Rule Take the Length of the Rafter for the bevel-Bevel-end in Feet and Inches and make it a Parallel in 15 then half the quantity of Feet and Inches Bevelling taken from the same Scale and carried parallelly till it stay in like parts shall shew right against it in the Tangents the Degrees and Minutes required And this is the Angle that the blunt corner is to be laid in Legement more than a square and the sharp Angle less than a Square or 90 Degrees both out of Level and out of square also when you tumble or stripe in the Tenons of the Purloins the thing desired Example Let AB represent the Bevel-end of a Frame being out of Square from the Line AC 6 foot as the Line CB sheweth then if AC be 20 foot AB will be 20 Foot 10 Inches Then draw EL the middle Line of the Frame and GM and HK the Lines at three quarter of the breadth of the Frame then take ED the half Bevel and lay it from G to F and from H to I and draw the Lines AF and BI for the outside Lines of the two bevel-Bevel-end Rafters end the two other Lines parallel to them according to the Breadth or Scantling of your Bevel-end Rafters as here in the figure 8 Inches broad Thus the Lines AF and BI represent the two end Rafters laid in Legement to fit in the Purloins as for their lying out of Square from the Raising-pieces And to the same Angle they are to be laid out at Level that the cutting of the Purloin ends may fit the Rafter sides when erected in their places according as the ends F and I of the Bevel-end Rafters are according to the Anglâ—s AFG and AFM the one being 11 degrees and 20 minutes under and the other 11 20 above 90 degrees Also Note that if PK and OM do represent a pair of square Rafters at any intended distance from A then T S and RQ will give the true Length of the Purloins fit for those places RQ being the shortest Purloin and T S the longest Purloin To find by the Rule only how long the Purloin must be on the outside more or less than the distance on the Raising-pieces where you intend the two Square Rafter feet shall stand do thus set the 30 Scales to the same Angle that the Bevel-end Rafters lie out of Square when they lie in Legement to frame which here is to 11 degrees and 20 minutes Then count from the Center the quantity of Feet and Inches you intend to make the Mortise-holes from the Rafter Foot in the Rafters for the Tenons of your Purloins and take from thence to the nearest distance to the other Line and that shall shew the quantity that the one Purloin is to be longer and the other shorter than the distance between the Rafter-feet on the Raising pieces Example thus Set the 30 Scales to the Angle GAF then count AS the place for the Mortise-hole from A on the Rafter and take the nearest distance from thence to the other 30 Scale that shall give SV the quantity how much T S is shorter than AO and how much RQ is longer than PB Note that if you count 3 quarters of 20 Foot 10 Inches being the Length of the bevel-Bevel-end that then you will make the Rafters too long by 4 Inches and a half as in the Figure you may see therefore the surest way to find the Rafters Length is to set the Scales to a Square and then to take the Parallel Extent from the Common Perpendicular to the ½ breadth between the place for the Rafter-feet on the Raising-piece So that the Length of the Rafters for the Bevel-end at true pitch is AF 15 Foot 3 Inches and not AW 15-7-½ which is just 3 quarters of AB the Bevel-end over which the two Rafters are to stand For then the top of the Bevel-end Rafters would be too high for the top of the Square Rafters being cut just 15 Foot three quarters of 20 Foot the breadth of the Frame Use XX. The Vse of the Scales to lay down or measure out on Paper
whereof he gave two to the Stairs and two to the Vacuity which had all their light from above and this in exact Oval is as a Master-piece You have here inserted the Types of several Stair-Cases with their Ichnography one whereof is a piece of Rarity being a pair of double Stairs whereon two persons the one ascending the other descending shall not come at one another made by Peidro del Bergo and Iehan Cosin at Sciamburg in France in the Kings Palace Describe a Semicircle for the Ichnography which divide in 12 equal parts and in it describe a smaller Cicle as at C. For the bigness of the Newel draw lines from those Divisions in the great Semicircle into the Semicircle made for the bigness of the Newel so will that Semicircle also be divided into 12 equal parts then on every of the points in the great Semicircle erect Perpendiculars and those Perpendiculars shall shew the ends of each respective step as the Perpendicular at 11 bounds the outward end of the first step the Perpendicular at 22 bounds the second step c. to 24 which makes good a whole Circle in the Ichnography and Perpendiculars erected from the inner Semicircle mark on the Newels the ends of the same steps work the same way with the steps on your right hand The Newel is pierced through in divers places to let in light Of Chimnies The Italians who make frugal fires are not in this case the best Counsellors therefore from them we may better learn how to raise fair Mantles within and how to disguise gracefully the shafts of Chimnies abroad therefore shall lay down the Observations of Phil. de l' Orme a man diligent in this part of work First he observeth that who in the disposition of the Building will consider the Region and the Winds that ordinarily blow from this or that Quarter might so cast the Rooms which need most fire that he should little fear the incommodity of Smoke But if the Error lies in the Structure it self then he makes a Logical Enquiry That either the Wind is too much let in above at the mouth of the Shaft or the Smoke stifled below If none of these then there is a repulsion of the Fume by some higher Hill or Fabrick that overtops the Chimny if likewise not this then he concludes that the Room is little and close so as the Smoke cannot issue wanting a supply of Air and so having a Natural Reason of the Cause we apply sutable Remedies Touching Conducts for the Suillage and other Necessities of the House which how base soever in use yet for the Health of the Inhabitants are as considerable as the rest I find in Authors this Counsel that Art should imitate Nature in those ignoble Conveyances and separate them from sight where there wants a running Water into the most remote and lowest and thickest part of the Foundation with secret vents posting up through the Walls like a Tunnel to the wiâ—d Air aloft Thus having considered the Apertions and Overtures according to their particular Requisites I come to the Contexture of the whole work under the term of Compartition into which being the mainest piece I cannot enter without a few general Precautions First Let no man that intendeth to build settle his fancy upon a Draught of the Work in Paper how exactly soever measured or neatly set off in perspective without a Model or Type of the whole Structure and of every parcel or partition in Board or Wood. Next That the said Model be as plain as may be without Colours or other beautifying lest the Pleasure of the Eye preoccupate the Judgment Lastly The bigger this Type is the better not that I would persuade a man to such an Enormity as that Model made by Ant. Labaco of St. Peters Church in Rome containing 22 foot in length 16 in breadth and 13 in height and costing 4184 Crowns the price of a reasonable Chappel Yet in a Fabrick of 30 or 40 Thousand pounds 30 pounds may be expended in an exact Model for a little Penury in the Premisses may easily breed some Absurdity of a far greater Charge in the Conclusion Now after these Premonishments I come to the Compartition it self by which is understood a graceful and useful Distribution of the whole Ground-plot both for Rooms of Office and of Reception or Entertainment as far as the Capacity thereof and the nature of the Country will comport The Gracefulness will consist in a double Analogy or Correspondency First between the Parts and the Whole whereby a great Fabrick should have great Partitions great Lights great Entrances great Pillars or Pilasters in sum all the Parts great The next between the Parts themselves not only considering the breadth and length as before when we spake of Doors and Windows but likewise their height a point hardly reducible to any general Precept True it is the Ancients did determine the Longitude of all Rooms which were longer than broad by the double of their Latitude and the Height half as much more as the Latitude which Dimensions modern Architects vary upon discretion sometimes squaring the Latitude and then making the Diagonal or overthwart Line from Angle to Angle of the said square the measure of the Height sometimes more but seldom lower than the breadth it self The usefulness consists in a sufficient Number of Rooms of all sorts and their apt Coherence without Distraction without Confusion that it may be well united and may appear airy and spiritous fit for the welcome of chearful Guests about which the greatest difficulty will be in contriving the Lights and Stair-cases in which respect the ancient Architects were at much ease for both the Greeks and Romans of whose private Dwellings Vitruvius hath left some Description had commonly two Cloistered open Courts one serving for the Womens side and the other for the Men who now adays would perchance take so much separation unkindly Howsoever by this means the reception of Light into the body of the Building was very prompt both from without and from within which we must now supply by some open form of the Fabrick or among graceful refuges by Tarrasing any story which is in danger of Darkness or lastly by perpendicular Lights from the Roof of all others the most natural For the second difficulty which is casting the Stair-Case which is no hard point of it self but as they are incumbrances of room for other use I have marked a willingness in the Italian Artizans to distribute the Kitchin Pantry Bake-house washing Rooms and even the Buttry likewise under ground next above the Foundation and sometimes level with the Floor of the Cellar raising the first Ascent into the House fifteen foot or more for that end which besides removing Annoys out of sight and gaining much room above doth also by the Elevation of the Front add Majesty to the whole Aspect and with such a disposition of the principal Stair-Case which commonly doth deliver us into the plain
and there comes on the 6 Columns between the modillions 26 spaces and of the 8 Columns the breadth must be 19 models and there comes on the 8 Columns 36 spaces between the modillions the height of the Lights of the Doors is 4 7 of the flat of the Column that come under the spaces of the modillions or in 6 parts under to the Architrave and the Light is of 6 ⅔ models the breadth of the Lights is 3 models and 5 minutes the Ornament must be ⅕ of the height of the Light and divided likewise in 15 of the like parts give 5 to the Architrave 4 the Friese and 6 the Cornish and the Architrave is 26 ⅔ minutes the Friese 21 ⅓ minutes the Cornish 32 minutes So the whole Ornament is 1 model 20 minutes XXVII The small Corinthian Arch must be 4 models 8 minutes wide from one Pilaster to the other the Pilaster is 26 minutes broad under on the Column the Impost is 33 ⅓ minutes high divided in 7 19 24 parts the height of the Arch or Bow is 25 minutes divided in 9 11 12 parts the Key-piece in the Arch is 50 minutes high the Arch is higher than one half-Circle 16 minutes the height from above the Impost to the under-edge off of the Base 7 models and 20 minutes XXVIII The Corinthian Gallery with the Pedestal the Column must be 15 ⅓ models high and the breadth of 4 Columns II models whereof the middle inter-Column must be 3 models the inter-Column on the side must be 2 models On the 4 Columns from the middle of the first to the middle of the last cometh 20 spaces and Modillions of 6 Columns breadth is 17 models and hath 32 spaces between the Modillions and of the breadth of 8 Columns is 23 models and hath 44 spaces between the Modillions the Light of the door is 4 7 of the under-edge of the Pedestal with his Column to the upper-edge of the Modillion and is 8 models 32 ½ minutes high the breadth of the Lights of the door is 3 models 59 ⅙ minutes the Ornament must be ⅕ of the height of the Lights of the doors and is 1 model 42 ⅖ minutes divided into 15 parts thereof the Architrave hath 5 parts and the Friese 4 and the Cornish 6 and the Architrave is 34 minutes the Friese 27 minutes the Cornish is 41 minutes XXIX If you will make the Corinthian Arch with the Pedestal then must the distance from one Pilaster to the other be 5 models the height from the under-edge of the Pedestal to the upper-edge of the Impost is 9 ½ models the Impost is high 55 1 12 minutes the bigness of the Arch must be 1 10 of the breadth like the foregoing Arch and is 30 minutes the Corner-piece 1 model the Arch is higher than one half Circle 20 minutes the height of the Lights of the door is 8 models and the breadth of the Lights of the door is 3 models 45 minutes the Ornament is high 1 model 36 minutes the Architrave hath 32 minutes divided in 9 ⅚ parts the Friese is 25 ½ minutes and hath one list of ⅕ part under the Cornish the Cornish is 38 ½ minutes divided in 5 ⅖ parts the Pilaster under on the Column is 30 minutes broad XXX Here followeth the particular members of the Corinthian Column On the right side you have the Pedestal and Base the Pedestal is ⅓ of the heighth of the Column and is 3 ⅓ models which divided in ⅞ 8 parts thereof give the under Cimacium 2 parts the Neck of the Pedestal 5 ⅞ parts the upper Cimacium 1 part the under Cimacium is 45 minutes thereof give the Plinth 30 minutes the other member is 15 minutes divided in 4 ⅛ parts on the Cimacium is also two members one Torus of ¾ and one list of ⅓ of the aforesaid parts the upper Cimacium is 22 ½ minutes divided in 7 ⅜ parts there under is one list of ⅜ parts goes off from the neck the Base is one half model divided in 6 ⅓ parts and must go off the shaft of the Column 1 ◠part and a ½ part On the left side is the Ornament and the Capital the Capital is high 1 model ⅙ or 70 minutes which divided in 23 ⅓ parts the Astragal is 1 ⅖ of the parts of the Capital The Ornament is ⅕ part of the Columns height and is 2 models this divided in 15 parts give 5 the Architrave 4 the Friese 6 the Cornish the Architrave is 40 minutes divided in 12 1 12 parts the Friese is 32 minutes the Cornish is 48 minutes divided in 7 3 120. So much it projects and is just 7 1 ◠parts XXXI Here followeth the great and small Impost with his Arch and Ornament of the principal Gate of the Corinthian Order On the right side is the Impost and Arch the Impost and Arch of the small Bow stands marked with the Letter K the Impost is high 33 ⅓ minutes divided in 7 19 24 parts The small Arch or Bow is high 25 minutes divided in 9 11 12 parts the height of the great Impost is 55 7 12 minutes divided in 7 13 120 the great Arch or Bow is 30 minutes divided in 9 11 12 parts On the left side is the Ornament of the principal Gate and is high 1 model 36 minutes thereof the Architrave hath 32 minutes divided in 9 5 6 parts the Friese is 25 minutes the Cornish 38 ½ minutes divided in 5 ⅖ parts XXXII Here is shewn how you shall lessen the Columns the Tuscan Column is ¼ smaller above than beneath the Dorick ⅕ the Ionick 1 ◠the Roman or Composita is 1 7 the Corinthian is ⅛ which are to be divided in 12 equal parts 3 of which must go up in a straight line in the Tuscan Column of the Ionick 3 ½ goes up in a straight line and the Corinthian 4 parts goes straight up of the Dorick and Roman or Composita is a measure between the Tuscan and Ionick and between the Ionick and Corinthian the other lessenings men may easily see how they shall make them in the Figure here set down XXXIII Shews how you may make the Corinthian Base and the upper and under Cimacium with his Diagonal lines for inlarging the Projecture XXXIV Sheweth how the Corinthian Ornament is to be made as the Architrave Friese and Cornice with his Diagonal lines for inlarging the Projecture easie to be understood so draw one Diagonal line after a perfect quadrate of the whole Projecture of the Cornice and in these Diagonal lines must all the Perpendicular lines come for the members that are in the Projecture and this outermost end must we then after this measure draw with the said Diagonal so that in the crossing you make right Angels that the height of the drawing members be parralel near to the Diagonal XXXV This is the Ornament of the Corinthian Order of the principal Gate and is 1 model 36 minutes high as before is declared
thereof the Architrave hath 32 minutes the Friese 25 ½ minutes the Cornish 38 ½ minutes the Architrave 32 minutes divided into 9 â…š parts thereof sticks farther out as the outer-edge of the Door-stile 7 â…” parts or 8 ½ minutes farther for Cornishing and let the ears of the Architrave be 17 parts long of the fore-given parts or 55 ½ minutes to underneath besides all other the Cornishing of the Architraves as you may see in the Figure the Friese is 25 ½ minutes divided in 7 parts for making the Voluta or Scroll and draw one line up the fourth part or 14 ½ minutes frome above off right Parallels so there remains 3 parts or 11 minutes for the standing out beneath and the eye of the Scroll is 1 7 part or 3 minutes and 2 14 of the height of the Friese and draw a Line perpendicular from above to the under-edge of the ear of the Architrave and where the lines cut cross each other here is the middle of your eye strike out the cross 4 parts 16 ½ minutes near to the outside and 3 ½ parts or 12 ½ minutes to the inside and draw your Scroll then after this manner here drawn the Scroll or Voluta beneath is â…• part 5 ½ minutes smaller as the upper-Scrol is and is high 20 minutes and the breadth 12 ½ minutes divide the height in 8 parts and draw a Parallel-line of 4 ½ parts or 11 ¼ minutes from beneath to above and there the Parallel-line cut cross the Perpendicular is the middle of the eye strikes out cross 3 ½ parts or 8 ¾ minutes to above and 4 parts or 10 minutes to the outside and there remains over 5 parts or 12 ½ minutes to the inside farther all that belongs to it may you in the Figure here plainly see as for the breadth of the Scroll is 2 â… parts of the Cornices given parts or 19 minutes the other members before may be seen in the Figure XXXVI Here is shown two Chimney-mantils with their Prosile XXXVII Here is shown the ground of the Building of the Lord Strozzi standing at Florence the like is described in the Authors third Book in the seventh Chapter XXXVIII The half of the Building on the ground to be seen inwards of the Building of the Lord Strozzi XXXIX The other half with the up-rising to be seen with the foreside of the foresaid Building XL. Here we have the under-side of the Cornice of all the five Columns A of the Tuscan B of the Dorick C the Ionick D the Roman or Composita E the Corinthian FINIS Advertisement THe Description and Use of the Carpenters Rule together with the Use of the Line of Numbers and its application in measuring all Superficies and Solids Gauging with the use of a sliding Rule and the Joynt Rule by Iohn Browne and sold by William Fisher. THE Description and Use Of an Ordinary JOINT-RULE Fitted with LINES For the ready finding The Lengths and Angles of Rafters and Hips and Collar-Beams in any Square or Bevelling Roofs at any Pitch and the Ready Drawing the Architrave Friese and Cornice in any Order WITH Other Useful Conclusions by the said Rule BY IOHN BROWNE LONDON Printed in the Year MDCLXXXVI The Description and Use of a Joint-Rule fitted with Lines for the ready finding the Lengths and Angles of Rafters Hips and Collar-Beams in any Square or Bevelling Roofs at any Pitch FIrst The Rule is an ordinary Jointed Rule of a Foot long when shut together or two Foot being opened to a straight Line And the Lines delineated thereon for this purpose are 1. First a Line of Lines drawn Sector-wise from a Center on both Legs of the Rule but continued to 30 at the end in stead of 10 the old usual manner and every single Integer of the 30 is divided into 12 parts to represent every particular Inch of the 30 Foot according to the common reckoning by Feet and Inches 2. There is another Scale of Equal parts also of the same length lying as near to the other of 30 as may be on one Leg only which is divided into 40 parts to represent 40 Feet and each of those 40 Feet parted into 6 parts to represent every two Inches only because the room for one Foot will not admit of more parts 3. In the same place on the other Leg is divided a Line of natural Sines and Tangents to 45 but numbred as a Line of Chords to 180 Degrees to set the Rule to or to find the quantity of any Angle in the proper terms of expression all the world over degrees and minutes 4. On the innermost Line of the 30 Scale that runs to the Center is set 20 pricks beginning at 2 at the Center-pin at 30 and so proceeding with 3 4 5 and 6 at the Center-pin at 15 and then 7 8 9 10 and so forwards to 20 towards the Center which serves to divide a Circle into any number of parts very useful and ready in the practice of Drawing or Architecture Thus much for Description the Uses follow The Uses of this Line of Lines or Scale of equal parts to 30 drawn from the Center is of a general and manifold use as Mr. Gunter in his Book of the Sector hath shewed A brief touch whereof take in the first place as by the way and then the use of the Rule to the business intended And for the better doing hereof it is needful to explain three or four terms for the avoiding of many words and needless repetitions in this brief yet plain Discourse 1. First by the word Lateral is meant any distance taken either in Feet and Inches on the 30 Scales or degrees and minutes on the Chords taken and counted from the Center in the midst of the head of the Joint-Rule along any one Leg as thus Suppose I would take out 15 Foot Laterally set one point of the Compasses in the Center at the head and open the other to 15 on any one Leg on the 30 Scale this extent I call a Lateral Extent of 15 Foot. Also if you take the Lateral Chord of 60 Degrees you shall find the extent of the Compasses from the Center to 60 to be the same as from the Center to 15 Foot on the 30 Scale of Feet and Inches 2. By the word Parallel I mean any distance taken by setting one point of the Compasses in any number of Feet and Inches on one Leg and the other point in the same or any other number on the other Leg across from one Leg to the other as thus the Rule being opened then the extent of the Compasses from 20 on one Leg to 20 on the other Leg is a Parallel extent 3. In all Parallel Extents you must set one point of the Compasses in the Common Line on one Leg to the Common Line on the other Leg which Common Line is that only of the 30 Scale which runs to the Center in which the Center-pins at 15 and 30 are 4. The nearest
distance from a point to a Line is only thus Set one point of the Compasses in the point given and open or shut the other being turned about till the other will but just touch or cleave the Line that I call the nearest distance Use I. To lay down a Line that shall represent any Number of Feet and Inches given or required Take the Number given laterally from the 30 or 40 Scale from the Center and that is the Line required But if these Scales are too great or too small then take your Number of parts and the length thereof Laterally As for Example suppose I would have 3 Inches to represent 30 Foot take out 3 Inches between your Compasses and make it a parallel in 30 and 30 and the 30 Scale is set to your desire Use II. To increase or diminish a Line to any Proportion Take the given Line between your Compasses and make it a parallel in the parts thereof then the parallel extent of the parts you would have it increased or diminished to is the Augmentation or Diminution which was required Example Let 3 Inches represent 8 Foot and to the same proportion I would have 10 Foot or 5 Foot viz. more or less Take 3 Inches between your Compasses and make it a parallel in 8 and 8 on the 30 Scale then the parallel distance between 5 and 5 doth diminish the Line and the parallel between 10 and 10 doth Increase the Line to the proportion required Use III. To divide a Line into any Number of parts or models under 30. Take the given Line and make it a parallel in the parts on the 30 Scale into which you would have it divided then the parallel extent between 1 and 1 shall divide the Line accordingly Example Let 4 Inches be a Line to be divided into 9 parts take 4 Inches or any distance whatsoever and make it a parallel in 9 and 9 on the 30 Scale then the parallel distance between 1 and 1 shall divide 4 Inches into 9 parts required Note that for more exactness and conveniency you may Double 9 or Triple 9 viz. 18 or 27 and then if you make the Line to be divided a parallel in Triple the Number you must take out 3 in stead of one and that shall divide the Line into the parts required Example I would have 5 Inches put into 10 parts take 5 Inches between your Compasses and make it a parrallel in 30 and 30 the Triple of 10 then take out parallel 3 and 3 the Triple of one and that shall divide the Line given being 5 Inches into 10 parts or models exactly the like for any other And note as the Rule stands you may take out any number of parts or models whatsoever to that Scale Use IV. Any two Lines given to find their Proportion one to another according to any other Number Take the Lines severally and lay them Laterally from the Center on the 30 or the 40 Scale which you please and the Numbers of Feet and Inches to which they reach shall shew their proportion one to another of the parts of the Line on which they are measured Example I have 2 Lines suppose one is 2 Inches long and the other 5 or any other unknown part Take 2 Inches the measure of one Line and measure it Laterally on the 30 Scale and it gives 5 Foot ½ an Inch then take out 5 Inches the supposed length of the other Line and it gives Laterally 12 Foot 8 Inches then I say one Line is 5 Foot and half an Inch and the other is 12 Foot 8 Inches of a Scale of 30 Foot in 11 Inches 3 quarters length Or if you conclude on the Term or number of one Line then make that Line a parallel in the parts thereof then take the other Line and carry it parallelly till it stay in like parts on both Legs in the common Line and that shall be the Denomination of the other Line Use V. Two Lines being given to find a Third in continual Proportion to them Take both the Lines and lay them laterally on both Legs and note the Feet and Inches to which they do extend as in the last Then take out the lateral extent of the second Line and make a parallel in the terms of the first Line keeping the common Line at that opening then the parallel extent from the terms of the second Line shall be the lateral 3d Term or Line in Proportion Example Suppose I have one Line 3 Foot long and another 5 Foot and I would have another to bear proportion to 5 as 3 doth to 5 increasing being in numbers thus as 3 is to 5 so is 5 to what Here note that 3 is the first number and 5 the second The first Line laid from the Center on the 30 Scale extends to 7 Foot 7 Inches and 5 Inches the second Line gives 12 Foot 8 Inches Now the lateral second Line viz. 5 or 12 Foot 8 Inches made a parallel 7 in Foot 7 Inches the terms of the first Line then take out the parallel extent from 12 Foot 8 Inches the measure of 5 and it shall give 21 Foot 1 Inch laid laterally from the Center for a third Proportional required which measured on the Inches is 8 Inches and a third the answer required for as 3 is in proportion to 5 so is 5 to 8 and a third part But by the Line of Numbers having the quantity of the Lines given in Numbers do thus The extent of the Compasses from the first Number 3 to the second Number 5 shall reach the same way from the second Number 5 to 8.33 the third proportional Number required Use VI. To divide a Line in such sort as another Line is divided Take the whole Line that is divided and lay it laterally on both Legs and fit the Line that is to be divided parallelly in the ends thereof then lay every part of the divided Line laterally in like manner as the whole Line was laid and the parallel extent between those parts shall divide the Line accordingly as for Example Suppose I would divide a Line of 8 Inches ¼ long in such sort as the Line of Circles on the inside of the 30 Scale is divided Take out 8 Inches ¾ and make it a parallel in 2 and 2 the divided Line then take out the parallel distance from 3 and 3 and that shall give the point 3 from the end of the Line you would divide and so consequently all the rest in order as far as you please Use VII To find a mean Proportional between two Lines or Numbers Open the 30 Scale to a right Angle by making lateral 21 Foot 2 Inches a parallel in 15 Foot. Then find the Sum and half Sum the Difference and half Difference between your two Numbers and having the half Sum between your Compasses set one Point to the half Difference counted laterally on one Leg and wheresoever the other Point shall touch the common Line on the other
of the House on one 30 Scale to the Common-line on the other 30 Scale is the nearest distance required being measured from the Center 16-7-½ Then take the whole Diagonal Line viz. CL or BK from the Center Laterally and make it a Parallel in the nearest distance last found and that shall set the 30 Scales to the Angle of the outside of the Hip required which you may measure in degrees thus take Parallel 15 as the Rule stands and lay it from the Center and it shall reach to 116 Degrees on the Chords next one 30 Scale the Angle of the outside of the Hips required Example and more briefly in a House 20 Foot broad The House-end is 20 Foot broad the whole Diagonal Line is 28 Foot 3 Inches â…œ the Hip-Rafter 18 Foot. Take 18 Foot between your Compasses and set one point in 20 and open or shut the Rule till the other fits 18 then the nearest distance from 20 to the Common-Line will be 16 Foot 7 Inches 4 8. Then take 28 Foot 3 Inches â… the whole Diagonal Line and make it a parallel in 16 Foot 7 Inches ½ the nearest distance and the 30 Scales are set to the Angles required For If you take out Parallel 15 the Chord of 60 and measure it Latterally from the Center it shall reach to 116 the Angle in Degrees and Minutes required Note If the whole breadth and whole Diagonal Line is too large for your Compasses then the half breadth and half Diagonal will do as well taking the half length of the Hip also between your Compasses and on the Scale also and that shall set the Scales to the same Angle as before Use XV. To find the Lengths and Angles of the Rafters and Hips or Sleepers in Bevelling Frames at any Piton 1. For the length of the Rafter set the 30 Scales square then count the half length of the bevel-Bevel-end on one Leg being always more there than the half breadth and the Perpendicular resolved on on the other Leg Then the Parallel distance between measured laterally shall be the length of the Rafter required and a Ruler laid to the two Points of the Compasses to set on the 30 Scales and a Bevel set as before in Square Frames is shewed shall give the Angles at head and foot required 2. For the Hips length count the Rafters length on one Leg and the half breadth of the bevel-Bevel-end of the House more by half the number of Inches bevelling on the other Leg and take the Parallel distance between and measure it laterally from the Center and it shall be the length of the longest Hip-Rafter And for the shortest Hip count less than the Bevel-end by half the number of Inches bevelling and that shall be the short Hip required 3. The Inches or Feet and Inches of Bevelling being given to and how much one corner is under and the other over 90 Degrees or just Square open the 30 Scales and take the breadth of the House over at the nearest distance between your Compasses from the 30 Scale from the Center laterally and make it a Parallel in 15 and 15 for 60 of the Chords Then take the Feet and Inches Bevelling from the same 30 Scale laterally and carry it Parallelly till it stay in like parts then just against it on the Degrees or Tangents are the Degrees and Minutes required that one corner is more and the other less than 90 Degrees 4. To find the Diagonal Line Take the distance in the Chords to the Degrees above or under 90 last sound from the Center laterally and make it a Parallel in 15 and 15 and then the 30 Scales are set to the Angle the end is over diagonal- or under 90 Degrees Then count the whole or half bevel-Bevel-end on both Legs and the Parallel distance between shall shew the length of the whole or half Diagonal Line measured from the Center Note That when the Rule stands at the Blunt Angle it gives the longest Diagonal Line and when it stands at the Sharp Angle it gives the shortest Diagonal Line 5. By the Diagonal Line and Perpendicular to find the Hips Length and the Angles at Head and Foot of the Hip or Sleeper Count the half Diagonal on one Leg and the Perpendicular height on the other Leg the 30 Scales being Square then the Parallel distance between shall be the length of the Hip required being longer or shorter as the Diagonal Line is Also a Rule laid to the two points of the Compasses measuring the Parallel Extent and a Bevel laid to the Rule and the two 30 Scales at each end gives the Angles at head and foot of Hips required To find the nearest Distance from the Corner of the Rombus to the opposite Hip set up in his true place 6. Count the length of the Hip on one 30 Scale and take that distance also between your Compasses laterally count also on the other 30 Scale the length of the Bevel-end and there set one point of the Compasses and open or shut the Rule till the other point falls in the length of the Hip-Rafter first counted then one 30 Scale represents the Raising-piece and the other the Hip set up then the nearest distance from the breadth of the Frame over at the Bevel-end and more or less by half the Feet and Inches Bevelling to the Common Line of the other 30 Scale being measured from the Center shall be the nearest distance required To find the Angle on the outside of the Hip. 7. To find the Outside Angle of the Longest Hip Take the shortest Diagonal Line between your Compasses and make it a Parallel in the nearest distance belonging to that Hip and the 30 Scales will be set to the Angle required and to measure it take Parallel 15 and 15 and measure it laterally from the Center in the Chords and you shall have the measure of the Angle required Example In a House of 20 Foot over at nearest distance and 4 Foot or 48 Inches Bevelling out of Square See Fig. II. Let ABCD represent a Frame 20 Foot over and 4 Foot Bevelling the Bevel end B C is longer than right over by 5 Inches for if you set the Rule square and take the Parallel extent from 20 the measure over to 4 Foot the measure of Bevelling and measure it Laterally you shall find it reach Laterally to 20 Foot and 5 Inches the true length of the Bevel-end The Bevel-end being 20 5 Inches the Perpendicular resolved on which at true Pitch ought to be about 11 Foot 5 Inches fere Then first for the Rafters Length 1. Set the 30 Scales square and set one point in 11 5 the Perpendicular and the other point in 10 Foot 2 ½ the half Bevel-end and to the Compass-points lay a Rule and to the Rule and the 30 Scales at both ends set a Bevel and one shall be the Angle at foot and the other at the Angle at the top of the Rafter
And the one Angle will be 42 Degrees for the Foot and the other 48 for the top of the Rafters and the measure between the Compasses measured from the Center shall be 15 Foot 4 Inches the Rafters Length required As by Inspection on the 40 and 30 Scales you may see 2. For the longest Hip set one point in 12 Foot 2 Inches and ½ more by two Foot than 10 Foot 2 Inch ½ the half Bevel-end and the other point in 15 4 the Rafters length and measure it from the Center it gives 19 Foot 6 Inches the longest Hip. Again Set one point in 8 Foot 2 Inches ½ 2 Foot shorter than the half Bevel-end by 2 Foot the half of 4 Foot the Bevelling and the other point in 15 Foot the Rafters length and measure it from the Center it gives 17 Foot 4 Inches the length of the shortest Hip. 3. For the length of both Diagonal Lines set the Scales of 30 to the Angle of the Frame at each corner and the measure from the half or the whole Bevel-end taken Parallelly shall be the length required of the half or whole Diagonal Line according as you take the whole or half bevel-Bevel-end As here in our Example the blunt-Blunt-end is 101 gr 30 min. or 11 30 more than 90 gr therefore take the distance from the Center to 101 diagonal- 30 on the Chords and make it a Parallel in 15 and 15 the Chord of 60 then is the 30 Scales set to the Angle of the blunt-Blunt-end of the Frame and the Parallel distance between 20-5 the whole bevel-Bevel-end gives 31 Foot 6 Inches the whole Diagonal Line B L or the Parallel between 10 2 ½ give 15-09 Inches B E the half Again The sharp end is 78 30 11 degr 30 less than 90 then the lateral Chord of 78 30 made a Parallel Chord of 60 at 15 then is the Rule set to the sharp end of the Frame for the shorter Diagonal Line And the Parallel distance between 10-2 ½ gives 12. Foot 11. the half or 25 Foot 10 Inches the whole Diagonal Line C F whose half is C E the shortest whole and half Diagonal Lines 4. For the Hips Length and Angles at Foot and Head. Set the 30 Scales square and count the shortest half Diagonal 12 Foot 11 on one Leg and the Perpendicular 11 Foot 5 on the other Leg then the Compass points so set lay a Rulâ— and take the Bevel at both ends and it shall give the two Angles at head and foot of the shortest Hip and the same distance of the Compass points shall be 17 Foot 4 Inches fere the Hip-lenght as before and the Angle at the top 48 30 and at Foot 41 30 his Complement Again Set one point in 15 Foot 10 the longest half Diagonal and the other point in 11 Foot 5 Inches the perpendicular and lay a Rule to them and set the Bevel to both ends and you shall find 54 gr the Angle at the top and 36 the Angle at foot and the distance between the Compasses laid from the Center gives 19 Foot 6 Inches the longest Hip. 5. For the Outside Angles of both Hips the longest first Take 19 6 between your Compasses the Hips length from the 30 Scale Set one point in 20 Foot 5 the Bevel-end and close the Rule till the other point touches 19 6 the Hips length Then take the nearest distance from 18 Foot 5 2 Foot less than 20 Foot 5 the breadth of the bevel-Bevel-end of the Frame to the other 30 Scale and it is the nearest distance from the point of the Rombus A to the Hip BG set up 15 Foot 9 Inches Then tâ—ke out 25 Foot 10 the shortest Diagonal and make it a Parallel in 15 9 the nearest distance and then the 30 Scales are set to the Angle required for the Outside of the Long Hip being 110 degrees for parallel 15 measured laterally on the Chord gives 1100. 6. For the Outside Angle of the shortest Hip. Take 17 Foot 4 Inches between your Compasses and set one point in 20 Foot 5 the Bevel-end and open or shut the Rule till the other point reaches 17 4 on the other 30 Scale Then the nearest distance from 22 Foot 2 Foot more than the breadth of the Bevel-end of the Frame to the Common Line on the other 30 Scale and that shall be the nearest distance from L to CG the shortest Hip set up which is 18 Foot 9 Inches Then take out 15 Foot 10 Inches the half greater Diagonal Line because 31 Foot 8 Inches is more than the Scale of 30 and make it a Parallel in 9 00 the half of 18 Foot and the 30 Scales are set to the Angle required viz. 122 degrees for if you take out Parallel 15 and measure it in the Chords laterally it shall be 122 the Angle required Note here by the way the length of the Bevel-end and the two Diagonal Lines and the halfs of them and the blunt and sharp Angles of the Frame are given by the draught of the Frame and they being first known the work is half done but if not given then use these Directions which will help you to see the reason of plain Triangles and the use of the Scales Use XVI To find the Rafters Hips and Angles in Bevel and Taper Frames being broader at one end than the other See Fig. III. First when the Frame is broader at one end than the other then the middle breadth is to be the guide for the Rafters Length and the Perpendicular to be equal to the middle Rafters perpendicular on both ends though one pair of Rafters is longer than another and the Roof in winding thereby Which winding may many times be remedied by some convenient artifice or other as the ingenious Workman will soon perceive As thus in brief Let ABCD represent the Frame of a House Bevelling at both ends and broader by 2 Foot at one end than the other as here in the Bevelling figure being 20 Foot on one side and 24 Foot on the other side at one Bevel-end 10 Foot 4 Inches and at the other end 8 Foot 1 Inch ½ but at the nearest distance over only 10 Foot and 8 Foot. First for your more apparent satisfaction draw the true form of the Frame by as large a Scale as you conveniently can with the Sides and Angles as exact as you can as ABCD then draw the middle Line EF quite through the length and GH through the breadth of the Frame Perpendicular one to the other then measure GH as suppose 9 Foot then lay off the half of GH from H to I and K then take out ¾ of GH and lay it from K and I to L 6 Foot 9 Inches for a pair of middling Rafters for this Taper-House LG being the common Perpendicular at the middle and both ends of the Roof 5 Foot 0 Inch â… of an Inch. And for the principal Rafters or other Rafters open the 30 Scale square and
comliest distance The contraction one seventh part In the Cornice both Dentils and Modiglions The Frize adorned with all kinds of Figures and various Compartments The Capital cut into one of the beautifullest leafs that Nature doth yield which is the Acanthas of Branca Vrsina Bears Foot. In short a Plainness did characterize the Tuscan so must Delicacy and variety the Corinthian Pillar besides the height of his Rank The last is the Compounded or Roman Order his name being a brief of his nature for this Pillar is nothing in effect but a medly of all the precedent Ornaments and though the most richly trimmed yet the poorest in this that he is a borrower of all his beauty His length a mean between the Ionick and Corinthian according to Scamozzi though some will have him the highest as of ten Diameters the contraction one eighth part less above than below his degree should be the highest but few Palaces ancient or modern exceed the third of the Civil Orders you may easily know him by the mixture of his Ornaments And so much touching the five Orders of Columns which I shall conclude with two or three not impertinent Cautions First that where more of these Orders than one shall be set in several Stories or Contignations there must be an exquisite care to place the Columns precisely one over another that so the solid may answer to the solid and the vacuities to the vacuities as well for beauty as strength of the Fabrick and by this Caution the consequence is plain that when we speak of the intercolumination or distance which is due to each Order we mean in a Dorick Ionical Corinthian Porch or Cloister or the like of one Contignation and not in storied buildings Secondly Let the Columns above be a fourth part less than below saith Vitruvius which doth appear a strange Precept and would seem reasonable rather to make them a fourth part bigger because according to the Optick Rule that the higher they are the less the diminution aloft should be because the Eye doth naturally contract all objects more or less according to their distance but Vitruvius acquits himself like a wise Mechanick the Natural reason before the Mathematical That therefore they above should be a fourth part less that those beneath may better sustain them A third Caution shall be That all the projected or Jutting parts as they are termed be very moderate especially the Cornices of the lower Orders for while some think to give them a beautiful and royal Aspect by their largeness they sometimes hinder both the light within and likewise detract much from the view of the Front without I need say no more concerning Columns and their Adjuncts only answer one familiar Objection It will perchance be said that this Doctrine touching the five Orders were fitter for the Quarries of Asia which yielded one hundred and twenty seven Columns of sixty foot high to the Ephesian Temple or for Numidia where Marbles abound then for the Spirits of England who must be contented with more ignoble materials To which I answer that this need not discourage us For I have often at Venice viewed with much pleasure an Antiporch after the Greek manner raised by Andrea Palladio upon eight Columns of the Compounded Order the Basis of stone without Pedestals the shafts or bodies of meer brick three foot and a half thick in the Diameter below and consequently thirty five foot high than which mine eye hath never yet beheld any Columns more stately of stone or marbles for the Bricks having been first formed in a Circular mould and then cut before their burning into four quarters or more the sides afterwards joyn so closely and the points concentre so exactly that the Pillars appear one entire piece which short description I could not omit that thereby may appear how in truth we want rather Art than Stuffe to satisfie our greatest fancies After Pillars the next in order are Pilasters touching which I will briefly collect these Notes Pilasters must not be too tall and slender lest they resemble Pillars nor too dwarfish and gross lest they imitate the Piles or Peers of Bridges smoothness doth not so naturally become them as a rustick superficies for they aim more at State and Strength than Elegancy In private Buildings they ought not to be narrower than one third nor broader than two parts of the whole vacuity between Pilaster and Pilaster but to those that stand at the corners may be allowed a little more Latitude by discretion for strength of the Angles In Theaters and Amphitheaters and such weighty works Palladio observeth them to have been as broad as the half and now and then as the whole Vacuity he noteth otherways and others consent with him that their true proportion should be an exact square but for lessening expence and inlarging of room they are commonly narrower in flank than in front Their principal grace doth consist in half or whole Pillars applyed unto them in which case it is well noted by Authors that the Columns may be allowed somewhat more than their ordinary length because they lean unto so good supporters And thus much shall suffice touching Pilasters which is a Cheap and a Strong and a Noble kind of Structure Now because they are oftner both for Beauty and Majesty found Arched than otherwise I am here orderly led to speak of Arches and under the same head of Vaults for an Arch is nothing indeed but a contracted Vault and a Vault is but a dilated Arch. Therefore to handle this business both compendiously and fundamentally I will resolve the whole business into a few Theorems Theorem 1. All solid Materials free from impediment do descend perpendicularly downwards because ponderosity is a natural inclination to the Center of the world and Nature performeth her motions by the shortest lines Theorem 2. Bricks moulded in their ordinary Rectangular form if they shall be laid one by another in a level row between any supporters sustaining the two ends then all the pieces between will necessarily sink even by their own natural gravity and much more if they suffer any depression by other weight above them because their sides being parallel they have room to descend perpendicularly without impeachment according to the former Theorem Therefore to make them stand we must either change their posture or their figure or both Theorem 3. If Bricks moulded or Stones squared cuneatim that is wedg-wise broader above than below shall be laid in a row level with their ends supported as in the precedent Theorem pointing all to one Center then none of the pieces between can sink till the Supporters give way because they want room in that figuration to descend perpendicularly But this is yet a weak piece of structure because the supporters are subject to much impulsion especially if the line be long for which reason this Form is seldom used but over Windows or narrow Doors therefore to fortifie the work as in this third