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25.

An universall principle of ye mechanicks 

When two weights or two other powers are disposed so that one canot be moved without moving the other, if ye space wch one of ye weights ought to run thrô according to its proper and natural direction is to ye space wch ye others ought to run thrô [[strikethrough]] ye [[/strikethrough]] in the same time according to its proper and natural function, reciprocall as ye last weight is to ye first; there shall be made an equilibrium between ye two weights, but if one is to ye other in a greater proportion it will force ye others. 

[[image: drawing of the bottom half of a semi-circle with the diameter labeled B A H G K, with a circle [weight or "bowl"] labeled E 1/8th of the way along the diameter line B K.  From A the midpoint of the diameter line there is a dotted line drawn vertically down the circumference of the semi-circle.  Also from A two lines [spokes?] drawn down to a point on the semi-circle labeled d and C.  Another dotted line is drawn down from H to d on the circumference; and another line is drawn down G to C and to a point beyond the semi-circle to point g.  Between lines A D and A C there is a short line h F e and next to it between lines H D and G g is a circle [weight or "bowl"] labeled b touching lines A C and G g at points e and f.]]

One may prove by this principall a surprising effect wch cannot be proved easily by other Hypothesis; viz that if there is many equall arms joyned to ye same [[?(ossiew)]] A as A B, A C, and a weight E is put upon ye arm A B and another b upon ye arm A C at the point F so that ye distances A E, A F may be equall ye weight in F being wound and not tyed to ye point F, so that it may roul from f to C but that it is hindered by a glass G C g placed perpendicular; then to make an equilibrium it is necessary that ye weight E be much more large than ye weight b, viz in proportion to B A G K,wch is contrary to what happens when ye weight F is tyed to ye inclined plane A F C for its then necessary to make an equilibrium that ye weight F may be greater than ye weight E in ye same proportion of E A to A H as hath been explained in ye preceeding figure.

To prove this paradox draw a line f b e horizontal passing thrô ye center of ye bowl b, if is evident that ye point E is higher than ye point of ye supporter F, and [[strikethrough]] shall [[/strikethrough]] that b e is somewhat longer than ye semydiameter b f;  but for to make ye demonstration ye triangle F h d is supposed infinitely small, and ye point F joyned to ye point e and that ye perpendicular F h passeth thrô ye point; now ye bowl b in descending shall be turned round ye point C by ye arc C A; and if d g is equall to ye diameter of ye bowl, Ye same arm shall be in ye situation A h d when ye diameter of that bowl shall be arrived to d g and ye point supporter F shall have described ye arc F h at ye same time as ye center of ye bowl shall be descended thrô a space equal to e d; but if because of ye smallness of ye arc there it taken ye arc F h for its tangent, one shall  have ye triangle F h d like to ye triangle A H F, and d F shall be to F h as F A or E A to A H, and because that ye weight E in proportion to ye Line  F h, ye space passed by ye bowl in descending directly from ye point F unto d shall be ye space passed in ye

Transcription Notes:
Reviewed The handwriting was difficult to read in some sentences. mandc: go back an read some of the previous transcriptions to catch on to the peculiarities of the archaic script and spelling. "r" looks like "u" some s's look like f's; j looks like i; hard to tell it from if. Which is abreviated wch, etc. The o with a dash over it can be typed by holding Alt down and typing 147 on the number keypad. The symbol appears when you release Alt. I don't change to correct spellings for words like "ye" to "the" "goeth" to "go" etc. [[?(ossiew)]] in another tranlation as appears as "axis." http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=11&pn=17&mode=imagepath This page took hours to transcribe.