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
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"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 15, 2024.
Pages
The conuerse of this proposition after Campane.
And if the two numbers, namely AB and CD be prime the one to the other. Then the lesse being continually taken from the greater there shalbe no stay of that sustraction, till that you come to vnitie. For if in the continuall substraction ther•• be a stay before you come to vnitie.* 1.1
[illustration]
Suppose that HA be the number whereat the stay is made, which also being subtrahed out of GC leaueth nothing. Wherfore HA measureth GC wher∣fore also it measureth FH by the 5. common sentence of the seuenth. And for as much as it also measureth i•• selfe, therefore it also measureth the whole AF by the sixth common sentence of the seuenth, wherfore also it measureth DG by the 5. common sentence. But it is before proued that it measureth GC, wherfore it measureth the whole CD, by the sixth common sentence of the seuenth: wherfore also it measureth BF by the 5. common sentence of the seuenth. And it is also proued that it measu••eth FA, wherfore also it measureth the whole number AB by the sixth common sentence of the seuenth. Now for as much as the number HA measureth the numbers AB and CD, therfore the numbers AB and CD are numbers composed: wherfore they are not prime the one to the othe••: which is contra••y to the supposition.
And by this proposition if there be two numbers geuen. It is easy to finde out, whether they be prime the one to the other or no.* 1.2 For if by such continual substraction of the lesse ••rom the greater, you come at the length to vnitie. Then are those numbers geuen prime the one to the other. But if there be a stay before you come to vnitie, then are the numbers geuen, numbers composed the one to the other.