Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.

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Title: Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S.
Author: Sturm, Johann Christophorus, 1635-1703.
Publication: London :: Printed for Robert Knaplock and Dan. Midwinter and Tho. Leigh,; 1700.
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Subject terms: Mathematics -- Early works to 1800.; Geometry -- Early works to 1800.; Algebra -- Early works to 1800.
Link to this Item: http://name.umdl.umich.edu/A61912.0001.001
Cite this Item: "Mathesis enucleata, or, The elements of the mathematicks by J. Christ. Sturmius ; made English by J.R. and R.S.S." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A61912.0001.001. University of Michigan Library Digital Collections. Accessed June 20, 2025.

Pages

Demonstration.

For the motion of the point A describing the semi-cycloid AFE, by Def. 11. is compounded of the motion of the orb (or wheel) B along the semi-circle ADC, and of the motion of the centre along the right line BC equal to CE, and conse∣quently to the semi circle it self, or motion of the orb, There∣fore as the point A moving to E by the motion of the orb (or wheel) moved or was carried from the diameter AC thro' the whole semi circle ADC 'till it came to AC again, and by the motion of the Centre passes thro' the whole space BG or CE, which is equal to the semicircular arch; thus the same A, when come to F, will have describ'd the quadrant AD, by moving from the diameter AC the quantity of the sine BD, and moreover by the motion of its centre (which is equal to the motion of the Orb) moves from AC the space of DF: And so the semiordinate BF will be equal to the arch AD and to its sine BD taken together; and in like manner the semiordinate bf will be equal to the arch Ad and its sine bd, &c. Q E. D.