Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	equal_a	line_n	1,364	5	9.1106	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A31370	New and rare inventions of water-works shewing the easiest waies to raise water higher then the spring by which invention the perpetual motion is proposed : many hard labours performed : and varieties of notions and sounds produced : a work both usefull profitable and delightfull for all sorts of people / first written in French by Isaak de Caus ... ; and now translated into English by John Leak.; Nouvelle invention de lever l'eau. English	Caus, Isaac de, 1590-1648.; Caus, Salomon de, d. 1626. Raisons des forces movvantes avec diverses machine.; Leak, John.	1659 (1659)	Wing C1527; ESTC R17548	33,436	91

divers Pinions and the same force moves them that Pinion shall give the most force to the Wheel to raise any weight whose number of teeth is the least But the said Wheel shall turn slower as hath been said And herein behold the Example If the Wheel A be turned by the Pinion C of 10. Teeth and be capable to raise a weight of 200. and instead of the Pinion of 10. teeth it be turned by a Pinion of 5. then it the force to raise 400. But as the weight is double in gravitie to the first so also it shall be as long again a raising up because the Pinion being 10. and the Wheele 100. the Pinion ought not to be turned above 10. times to make a whole turn or revolution of the Wheel But if the Pinion be 5. it must make 20. turns before the Wheel makes one because the number 5. is contained 20 times in 100. And so as the Pinion C is double to the Pinion F the weight raised by F shall be double to the weight raised by C And the time of the raising it shall be also double PROP. 15. If two Wheels are equal in Form and Matter and there be unequal Weights fastened to their Ax-trees they cannot be moved by the same Force in the same Time THis Proposition doth in some sort result from the former as may be seen in the Demostration Let there be two equal Wheels D and F of 96. Teeth and let there be fastened to the Axis G a weight of 300 and to B one of 400 and let it be supposed that the Pinion T of eight teeth moves the said weight by the means of the force of one Man It is certain that if there be put to the Wheel F a Pinion equal to T that the same Man or the same Force which was onely made to turn T will not suffice to turn a Pinion equal to it in the Wheel F because of the weight V which is heavier then M If then you would move the Weight V by the same force you must put to the Wheel F a Pinion which hath such proportion to T as the weight M hath to the weight V. Now the Pinion T being of 8. the Pinion X must be of 6. because that there is the same rate of 8. to 6. as of 400. to 300. and the same Pinion X of 6. teeth being moved by the force aforesaid the weight V shall be raised but not in the same Time because there are made but 12. Turns of T to make one Turn of D and there must be 16. Turns of X to make one Turn of F. PROP. 16. If two unequal Weights be put to the ends of the Beam of a Ballance and if they be hanged on a point which divides the Beam into two parts having the same rate the one to the other in length as the said weights have in heaviness Those weight although unequal shall be in equal ballance if the lighter be put to the end of the longest part of the Beam LEt the unequal Weights be D and E and let D be 15. pound weight and E 6 I say that they being at the end of the Beam of the ballance AB if they be hanged on a point as C so as the part AC may have such proportion to the part CB as the weight E to the weight D D being at the shortest distance from the center of the Beam shall not weigh more then E which is at the longest end because the weights are heavie in proportion according to their distance from the point on which the Beam of the ballance is hanged Now if the Beam of the ballance be divided into 7 parts there shall be 5. parts on the one side of the Center and 2. on the other which are in the same proportion as the Weights 15. and 6 because 6. is the two fifts of 15 as 2. is of 5. And if the difference of the Weights D and E were greater or lesser they shall alwaies be in equal Ballance if the Beam be hanged from a point which divides it as is before said You may see other Examples in the Figures following P which differ from this A Corollarie From hence it follows that two equal Weights are not alike heavie if they be put at the end of a Beam which is hanged from unequal parts And it must be observed that although the two sides of the Beam are in equal ballance if they are of unequal length equal weights shall weigh unequal As for example If the Beam AB be hanged in C so as CB may be longer then AC by a fourth part and yet AC and CB be in equal ballance because the part AC is thicker then the part CB yet if the equal weights D and F be put to the ends of the Beam AB the weight F shall weigh a fourth part more which is the difference of BC and AC PROP. 17. The manner to shut and open the Cocks of the Phneumatique Engin by the means of Water IN the Construction of the Phneumatique Engin which causeth Water to mount higher then the Spring There is required a Vessell which ascends and descends by means of the Water to turn the Cocks therefore I have put here certain examples among which you may chuse the most convenient both for that Engin and for the other Engins Now behold the effect of the Vessel in which there is a Syphon which shall be something lower then the height of the Vessel and the said Syphon shall be larger then the Pipe which gives Water to the Vessel when M is emptie the weight L shall turn the Cock towards it but when the Pipe H hath filled M then the said M weighing more then the weight L shall draw back the Cock towards it self and then the Syphon begining to run shall make M lighter then the weight L and so the Cock shall be turned back again There may be also made another Vessel as F which may be so hanged upon the handle as it may be moveable upon two Pins and may over-turn and emptie the water when it is full And to perform this the Pins must not be diametrically opposite but more towards one side then towards the other Now because the said Vessel being emptie should return of it self the counter-poise E must be put to the lighter side to ballance it equally this being done if there be a weight as hath been said in the aforegoing Proposition which shall be heavier then F that Vessel F shall be at the highest when it is empty but when it is half full being heavier then D the said Vessel shall descend towards F and being full it shall emptie it self towards X and being emptie it shall be again lighter then the Weight and return to its first place where it shall be till it be filled again to descend The reason of the emptying may be gathered from the Corolarie of the 16. Proposition There may be also made

Pipe and the bottom of the said Box there is a smal Pipe which shall let Water into the Basin marked with S Which shall be fastned to two turning Buckets marked VT so as when the Vessels shall be ful of Water that it may be heavier then the cover of the Valve R and on the contrary when the said Vessel shall be void the cover of the said Valve must be heavier to the intent that it may shut and draw the said Vessel up and so when the Water shall run into the said box by the Pipe V it shall rise up to the Pipe O and fall upon the side of the water Wheel L then the said Wheel turning shall turn I and consequently the Axtree IH so as the Chain shall turn about I and unturn H then the Figure of Galatea shall move towards the Pully E because it is drawn thither by the said Chain which turns about the Ax●ree I the smal Vessel S must be so proportioned that being fed by the smal Pipe it may be full or near full and draw up the Valve when the Figure of Galatea shall be near the Pully E and then the Water which shall be in the said box shall fall by the Valve upon the other side of the water Wheel and make it turn the other way so as the Chain H must turn about the Axtree on the side H and unturn on the side I which will be the cause to make the Figure turn toward the motion and so the Pully B shall be drawn upon which the Figure is placed sometimes forward and sometimes backward according as the double water Wheel shall turn sometimes by the Water that runs by the Valve R and sometimes by that which runs by the Pipe O which is done divers times by means of the smal Vessel S and the turning Buckets T and V for when the Vessel S is empty the Valve R is shut and the Water riseth up to the P●pe O to make the water Wheel turn one way and when S is full it opens the Valve and then all the water fals by the Valve R on the other side of the water Wheel which makes it turn the other way and so successively As concerning the Cyclope playing upon the Flajolet the motion shall be shewed in the following Figure It is to be noted that the little box marked with P is here represented open on one side to the intent to sh●w the Valve R. The Explanation of Plate XVI An Engin by which the Sound of the Flajolet shall be represented by the course of the Water HEre shall be represented the Engin proper to make the Flajolet Sound to the Cyclope of the precedent plate Therefore let there be a Musical Wheel marked with A about 4 or 5 foot in Diameter perfect round and divided with Teeth as you may see in the Figure so as a Pinion of 8 Teeth marked with B may turn the said Wheel and to the Arber of the said Pinion there shall be a Wheel having 32 Teeth marked with D which another Pinion marked with C shall turn and to the Arber of the said Pinion C there shall be a water Wheel marked with F about 2 foot and a half or 3 foot in Diameter which shall be turned by the water descending from the Pipe G and so when the said water Wheel shall turn it shall cause the Musical Wheel to turn by means of the other Wheels afterwards there shall be put the Summer marked with H the Fabrick whereof shall be shewn at large so as the Keys of the said Summer shall be Parallel at half an inch dist●nce from the Musical Wheel afterwards div●de the said Musical Wheel in 25 or 30. equal parts each part in turning shall be an ordinary measure of Musick and more-over all the said parts shall be divided into 8 equal parts to put on Crochets upon each division if it be required of which there are 8 for one measure and if you will you may put on Demi Crochets or Quavers afterwards the pins are to be put upon the said Wheel ¾ of an inch above the Superficies of the said Musical Wheel so as when the Wheel shall turn the said pins may touch the Keys of the Summer and put them down and cause them to open the Valvs of the said Summer as concerning the Pins they shall be put according to the Tune that you desire the Flajolet to play That which is here set down begins thus And when you would change the Tune it may be done by dismounting the Pinion B out of the Musical Wheel by means of the Rest of Iron upon which the Pinion shall be put and loosning a smal Screw which holds the said Rest in its place then the said Rest being drawn from its hole the said Pinion shall be disjoyned from the Musical Wheel which may be turned with the hand you may fit any other Tune upon the said Wheel the 12 holes that are in the Summer serves to conveigh the wind of the said Summer by the conveiances of Copper or Lead to the Organ Pipes to represent the Sound of the Flajolet all which shall be joyned to the Figure of the Cyclope The construction of the said Pipes shall be taught hereafter the hooks which hang at the Cords PO serve to draw up the Musical Wheel that if there be any fault in the Valves within the Summer it may be helped by opening the said Summer before as is done ordinarily the great conveiance marked with S may be of Wood 4 inches square to conduct the Wind to the Summer which shall come from the Bellows as shall be taught The Explanation of Plate XVII IN this Plate is represented the Figure of Neptune which shall turn Circularly with certain Trytons and other Figures which shall cast forth Water in turning The Wheel work belonging to the motion of these Figures shall be declared in the following Plate The Explanation of Plate XVIII This Plate declares the motion and Wheel-work of Neptune and other figures represented in the foregoing Plate LEt there be a water Wheel marked with A which turning shall turn a Toothed Wheel marked with B the Pivot whereof shall rest upon a straight peece of wood and the Arber above marked with PQ shall be fastned firmly to a Pipe of Copper marked with SR and at the end thereof there shall be a smal Receiver where the water shall fall Then there shall be a great Pipe marked with TV which shall be also fastned to the Arber a little lower then R so as the said Pipe may turn upon another marked with pointed lines which shall be interlaced marked also with pointed lines and the said great Pipe and that in the middle shall be Soldered firmly to the bottom of the Reserve of Lead maked with CD and the great Pipe XV shall be Soldered to a great Wheel marked with EF which shall be within two inches of the bottom of the said Reserve so as when