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 6, 2024.
Pages
* 1.1An inordinate proportionality is, when as the antecedent is to the consequent, so is the antecedent to the consequent: and as the consequent is to an other, so is an other to the ante∣cedent.
This definition also as the other before, requireth two orders of magnitudes, Suppose in the first order that the antecedēt A be to the cōsequēt B, as the antece∣dēt C,* 1.2 in the second
[illustration]
order is to the conse∣quent D, & let B the consequēt of the first proportiō be to some other, namely, to the magnitude E, as some other, namely, the magnitude F, is to the antecedent C of the second proportiō:* 1.3 this kinde of proportionalitie is called inordinate or perturbate.
[illustration]
Take also an example in numbers, as 9 to 6. the antecedent to the consequent, so is 3 to 2 the antecedent to the consequent, ei∣ther proportiō is s••squ••ul tera, and as •• the consequent of the first
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proportion, is to an other, namely, to the number 3. so is another namely, the num∣ber 6. to 3. the antecedent of the second proportion, for eyther is dupla propor∣tion.