On the Movement of Animals, Part Two (1681) - Page 22

PROPOS. X.

a Tab. 15. Fig. 6.

The same things being posited , if the corrugation of the rope is perfected so that DFC is parallel to BG and AE, as well as to the directions DS and CR: the opposite powers S and R will be quadruple of the weight Z.

Because the opposite directions RC, SD, as well as the ropes AC, CD, and BD, are parallel to each other: therefore the angles and triangles GDF and FCE are entirely destroyed; and thus the lines DO, DG, DF, CF, CI, CE are equal to each other; wherefore the sine DO taken four times will be the quadruple of one DG. Therefore, the two powers S and R have the same proportion to Z as 4 to 1, etc.

SCHOLIUM

a Tab. 15. Fig. 7.

Corrugation of this kind can be effected in another way, if, namely, the intermediate part of the rope DFC is revolved around a rod MN, and then likewise the two opposite powers S and R, by twisting the rod, create the spiral GDFCE, and likewise the two powers S and R will be quadruple of the weight Z.

PROPOS. XI.

a Tab. 15. Fig. 8.

The same things being posited, if the intermediate rope is perfectly corrugated many times at C, D, E, F by the powers SR, HI, KL, MN. I say that all the corrugating powers have the same proportion to the resistance Z as the multitude of corrugations C, D, E, F taken four times has to unity.