The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed
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Title
The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed
Author
Euclid.
Publication
Imprinted at London :: By Iohn Daye,
[1570 (3 Feb.]]
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Subject terms
Geometry -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A00429.0001.001
Cite this Item
"The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A00429.0001.001. University of Michigan Library Digital Collections. Accessed June 14, 2024.
Pages
¶The 35. Theoreme. The 40. Proposition. If a number haue any part: the number wherof the part taketh his deno∣mination shall measure it.
SVppose that the number A haue a part, namely, B: and let the part B haue his denomination of the number C. Then I say, that C measureth A. Let D be vni∣tie. And forasmuch as B is a part of A, hauing his denomination of C:* 1.1 and D being vnitie is also a part of the number C, hauing his denominatiō of C: there∣fore what part vnitie D is of the number C, the same part is also B of A:
[illustration]
wherefore vnitie D so many ••••••es measureth the number C,* 1.2 as B measu∣r•••••• A. Wh••ref••re ••••••ern••••ely (by ••••e 15. ••f the s••••••nth) vnitie D so ma∣ny ••••mes m••••••••reth the nu••••be•• B, 〈◊〉〈◊〉 C meas••••eth A. Wheref•••••• C mea∣sureth A: which was requi••••d to b•• proued.
This Proposition is the conuerse of the former: and the meaning therof is, that e∣uery number hauing a third part is measured of three, and hauing a fourth part is mea∣sured of foure. And so forth.