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 7, 2024.
Pages
¶ The 29. Theoreme. The 29. Proposition. I•• an odde number multiplying an odde number produce any number, the number produced shalbe an odde number
SVppose that A being an odde number multiplying B being also an odde number, doo produce the number C. Then I say that C is an odde number. For forasmuch as A multiplying B produced C, therefore C is composed of so many numbers equall vnto B as there be vnities in A.* 1.1 But either of these num¦bers
[illustration]
A and B is an odde number. Wherefore C is com∣posed of odde numbers, whose multitude also is odde. Wherfore (by the 23. of the ninth) C is an odde nūber: which was required to be demonstrated.
A proposition added by Campane.
* 1.2If an odde number measure an euen number, it shall measure it by an euen number.
For if it should measure it by an odde number, then of an odde number multiplyed into an odde number should be produced an odde number, which by the former proposition is impossible.
An other proposition added by him.
* 1.3If an odde number measure an odde number, it shall measure it by an odde number.
For if it should measure it by an euen number, then of an odde number multiplyed into an euen number should be produced an odde number which by the 28. of this booke is impossible.