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 8. Proposition.
If a number be deuided into two equall part••s, and if vnto it be added an other number: that which is produced of the multiplication of the whole being composed into the number added, to∣gether with the square of the halfe, is equall to the square of the number composed of the halfe and the number added.
This proueth in numbers that which the 6. of the second proued touching lines. For suppose that the number AB be deuided into equall numbers, which let be AC and CB: and vnto it•• adde the number BD.* 1.1 Then I say, that that which is produced of the whole AD into DA together with the square of BC, is equall to the square of CD. For by the 6. of these
[illustration]
propositiōs the square of CD is equal to the square of DB, & to the square of BC, and to that which is produced of DB into BC twise. But by the ••. of these propositi∣ons,* 1.2 that which is produced of BD into himselfe and into BC twise is equall to that which is produ∣ced of BD into DA (for AC and CB are equall) wherefore the square of CD exceedeth that which is produced of BD into DA by the square of CB. Wherefore that is manifest which was required to be proued.