Selected quad for the lemma: mind_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
mind_n	line_n	page_n	read_v	1,636	5	9.6665	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29761	The description and use of the trianguler quadrant being a particular and general instrument, useful at land or sea, both for observation and operation : more universally useful, portable and convenient, than any other yet discovered, with its uses in arithmetick, geometry, superficial and solid, astronomy, dyalling, three wayes, gaging, navigation, in a method not before used / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5041; ESTC R15524	175,812	507

stor'd As first with Gunters Sector and his Quadrant eke also By Foster altred after and with Gunters Rule and Bow The Traviss Quadrant and Cross-staves the Davis Quadrant too Their uses all to more than halfs this Instrument will do With this advantage more beside of lying in less room A fault that Saylors must abide when they on Ship-board come In the next place the Rudiments of Geometry exact The right Sines ●heir complements and how they lie compact Within a Circle and the rest the Chords and versed Sines About a Circle are exprest the Tangents Secants Lines And how their use and place is seen in Round and Plain Triangles Which serve to deck Urania Queen as Iewels Beads and Spangles In the next place Arithmetick by Numbers and by Lines In wayes that won't be far to seek by them that use their times Because the Precepts are explain'd by things of frequent use That for the most part are contain'd in City Town or House As Land and Timber Boards Stones Roofs Chimneys Walls and Floor Computed and reduc●d at once in Thickness Less or More The cutting Platoe's Bodies five which are not yet made six And them the best way to contrive and Dials on them fix Their Measure and their Magnitude in Circle circumscribed Whose Properties by old Euclide and Diggs have been described Then also in Astronomy are many Propositions Which fitly to th' Rule I apply avoiding repetitions And after in the pleasant Art of Shadows I do wander To draw Hour-lines in every part both upright over and under And all the usual Ornaments that on Sun-Dials be Which are describ'd to the intent Sol's travels for to see As first his Place and Altitude his Azimuth likewise His Right Ascention Amplitude and how soon he doth Rise The same also to Moon and Stars is moderately appli'd Whereby the time of Night appears the Moons Age and the Tide Then Heights and Distances to take at one or at two Stations Performed by those wayes that make the fewest Operations And also ready Rules to use the Logarithmal Table Which may prove ready Hints to these that are in those most able And many other useful Thing is scattered here and there Which formerly by Me hath been accounted very rare And lastly for the Saylors sake I have spent many an Hour Th' Trianguler-Quadrant for to make more useful than all other Sea Instruments that they do use at Sea for Observation And sure I am it won't abuse them in their Operation As in the following Discourse to them that willing be It will appear with easie force if they have eyes to see The Method and the Manner us'd as neer as I was able To follow the old Wayes still us'd and counted warrantable And in this having done my best 〈…〉 up my male Ascribing to my self the least would have the Truth prevail And give the honour and the praise to him that hath us made Of willing minds his Fame to raise by his assisting aid To whom be honour now and eke henceforth for evermore Ascribed by all them that seek the Truth for to adore J. B. ERRATA PAge 28. line 8. for Rombords read Romboides P. 73. l. last f. 337 r. 247. p. 75. l. 1. f. 7. r. 8. p 87. l. 14. r. multiplied by p. 89. l. 14. f. 5 371616. r. 538.1616 l. 21. f. 537 r. 538. p. 90. l. 4. f. 537 r. 538. l. 5. add being better done with a parallel answer p. 100. l. 2 add the Thred p. 128. l 2. dele 10 min. p. 133. l. 6. f. 60 r. 16. p. 143. l. 10 11. f. from 12 to 7 r. from 7 to 12. p. 146. l. 22. f 12 Section r. 13 Section p. 158 l. last dele and. p. 160. l. 11. f. 72 r. 720 also in line 15 23. p. 164. l. 19. f. Diameter r. Area p. 165. l. last add to 707. p. 184. l. 10 f. foot r. brick l. 20. f. ½ r. 1 ½ p. 187. l. 17. f. Ceiling r. Tileing p. 201. l. 11. f. 52 Links r. 55 Links l. 12. f. 48 Acres r. 4 Acres 3 Roods 8000 Links p 102. l. 5. f. 21 Acres 42 Links r. 2 Acres 0 Roods but 14760 Links read so likewise in l. 11. of the same page p. 204. l. 1. f. 16 ½ r. 18 ½ p. 205. l. 8. f. 55 r. 50. r. 50 f. 55 in l. 21 22. p. 206. l. 19. f 4-50 r. 4-50000 l. 21. f. 1 Chain 25 r. 11 Chains 23. p. 229. l. 16. f. 8-10 th r. 8-100 p. 231. l. 15. f of r. at p. 234. l. 22. f. 1 of a foot r. 1.10 th of a foot p. 236 the 3 lines over 134-5 are to come in after 134-5 Also the two lines over 3-545 should come in after 3-545 p. 257. l. 13. f. ●496 r. 249-6 p. 370. l. 3. f. sine r. Co-sine p. 383. l. 22. add by the general Scale p. 384. l. 14. f. = S. ☉ r. = Co-sine p. 414. l. 11. f. or r. on p. 420. l. 22. f. 71 r. 31. p. 429. l. 15. f. Declination r. Suns Right Ascention The Description and some Uses of the Triangular Quadrant or the Sector made a Quadrant being an excellent Instrument for Observations and Operations at Land or Sea performing all the Uses of the Fore-staff Davis-Quadrant Gunter's-Bow Gunter's-Cross-staff Gunter's-Quadrant and Sector with far more conveniency and as much exactness as any or all of them will do The Description thereof 1. FIrst it is a joynted Rule or Sector made to what Length or Radius you please as to 6 9 12 18 24 30 or 36 inches Length when it is folded or shut together the shorter of which Lengths is big enough for Land uses or Paper draughts the four last for Sea uses or Observations To which is added a third Piece of the same length of the Sector with a Tennon at each end to fit into two Mortice-holes at the two ends of the inside of the Sector to make it an Aequilateral Triangle from which shape and its use it is properly called a Triangular Quadrant 2. Secondly as to the Lines graduated thereon they may be more or less as your use of them and as the cost you will bestow shall please to command But to make it compleat for the promised Premises these that follow are necessary to be inscribed thereon as in the Figure thereof And first you are in order hereunto to consider The outer-edges of the Sector or Instrument the inner-edges the Quadrantal-side the Sector-side and the third or loose-piece also the fixed or Head-leg the moving-leg the head and the end of each leg also the head and leg center of which more in its proper place 1. And first on the outer-edge is placed the Lines of Artificial Numbers Tangents Sines and versed Sines to as large a Radius as the Instrument will bear 2. Secondly on the in-side or edge on short Rules is placed inches foot measure the line of 112

Surveying and Dialling Sect. VI. To divide a Line into any Number of Parts Take the whole length of the Line between your Compasses and setting one Point in the Number of Parts you would have the Line divided into with the other lay the Thred to ND and there keep it then take the ND from 1 to the Thred and that shall divide the Line into the parts required Example Let AB be to be divided into 7 parts Take AB make it a Parallel in 7 laying the Thred to the ND there keep it then the = 1 shall divide the Line into 7 parts But if the Line were to be divided into many parts as suppose 73 Then first fit the whole Line in = 73 then take out the = 72 71 70 for the odd 3 then the = 10 s. for every 10th division then the = 1 for the smaller parts or else you shall find it almost an impossible thing to take at once any distance which being turned above 50 times over shall not at last happen to be more or less than the desired Number required Note That if the given Number happen to be such that the Part will fall too near the Center as suppose 11 12 or any Number under 30 then you may double treble or quadruple the Number and then count 2 3 or 4 for one of the Numbers required As for Example Suppose I would divide a Line into 15 parts multiply 15 by 6 and it makes 90 Now in regard you have multiplied 15 by 6 you must take the = 6 instead of the = 1 to divide the Line into 15 parts between your Compasses because the whole Line is set in = 90 instead of = 15 which is 6 times as much as 15. Note also if the Line be too big for your Scale then take half or a third and make it a = in the given Line then take out the = 1 and turn two or three times to divide the Line according to your mind when it is too large for your Scale These two last are not to be done by the Line of Numbers but proper for the Line of Sines only unless you turn your Lines to be divided into Numbers and then work by Proportion as thus As the whole Number of Parts is to the whole Line in any other parts So is 1 to as many of those Parts as belongs to 1. Sect. VII To find a mean Proportion between two Lines or Numbers given A mean Proportion between two Lines or Numbers is that Number which being multiplied by it self shall produce a Number equal to the Product of the two Numbers given when they are multiplied the one by the other Example Let 4 and 9 be two Numbers between which a Geometrical mean is required 4 and 9 multiplied together make 36 So also 6 multiplied by it self is 36 Therefore 6 is a mean Proportional between 4 and 9. To find this by Arithmetick is by finding the Square-root of 36. But by the Line of Numbers thus Divide the distance between 4 and 9 into two equal parts and the middle-point will be found to be 6 the Geometrical mean proportional required But to do it by the Line of Lines do thus First joyn the Lines or Numbers together to get the sum of them and also the half sum and substract one from the other to get the difference and half the difference then count the half difference from the Center down-wards and note where it ends then taking the half sum between your Compasses lay your Thred to 00 on the loose-piece then setting one Point in the half-difference on the Line of Lines See where on the loose-piece the other Point shall touch the Thred and mark the place with a Bead on the Thred or a speck of Ink or otherwise for the measure from thence to the Center is the mean Proportional required Or else use this most excellent way by Geometry Draw the Line AB and from any Scale of Equal Parts take off 4 and 9 and lay them from C to A and B then find out the true middle between A and B as at E and draw the half Circle ADB then on C erect a perpendiculer Line as CD then if you take CD between the Compasses and measure it on the same Scale that you took 4 and 9 from and you shall find it to be 6 the true mean proportional required being only the way by the Line of Lines as by considering the Triangle CDE will appear To do this by the Sector open the Line of Lines to a Right-Angle by 3 4 5 or 6 8 10. thus Take 10 Latterally between your Compasses make it a Parallel in 6 and 8 then is the Line of Lines opened to a Right-Angle or if your Rule be large and your Compasses small then take Latteral 5 the half of 10 and make it a Parallel in 3 and 4 the half of 6 and 8 and it is rectangle also Then set half the difference on one Leg from the Center then having half the sum between your Compasses set one Point in the half-difference last counted and turn the other Point to the other Leg and there it shall shew the mean proportional Number required 1. To make a Square equal to an Oblong Find a mean proportion between the length and the breadth of the Oblong and that shall be the side of a Square equal to the Oblong Example Let the breadth of the Oblong be 4 and the length 9 the mean proportion will be found to be 6 Therefore a Square whose side is 6 is equal to an Oblong whose breadth is 4 and length 9 of the same parts 2. To make a Square equal to a Triangle Find a mean proportion between the half Base and the whole Perpendiculer and that shall be the side of a Square equal to the Triangle Example If the half-Base of a Gable-end be 10 and the whole Perpendiculer 11-18 the mean proportion between 10 and 11-18 is 10-575 the side of the Square equal to that Triangle or Gable-end required 3. To find a Proportion between the Superfecies though unlike to one another First to every Superfecies find the side of his equal Square whether it be Circle Oblong Romboides or Triangle then the proportion between the sides of those Squares shall be the Proportion one to another Example Suppose I have a Triangle and a Circle and the side of the Square equal to the Circle is 10 inches and the side of the Square equal to the Triangle is 15 inches The Proportion between these two Squares as they are Lines is as 10 to 15 but as Superfecies as 100 to 45 being thus found out Take the Extent between 15 and 10 on the Line of Numbers and repeat it two times the same way from 100 and it shall reach to 45 the Proportion as Superfecies between that Circle and Triangle whose Squares equal were 15 and 10. 4. To make one Superfecies equal to another Superfecies of another shape but