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

About this Item

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.]]
Rights/Permissions: To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
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 15, 2024.

Pages

A proposition added by Flussas.

If a Sphere touche a playne superficies•• a right line drawne from the center to the touche, shall be erected perpendicularly to the playne superficies.

Suppose that there be a Sphere BCDL: whose centre let be the poynt A. And let the playne su∣perficies GCI touch the Spere in the poynt C, and extend a right line from the centre A to the poynt C. Then I say that the line AC is erected per∣pendicularly

[illustration]

to t••e playne GIC. Let the sphere be cutte by playne superficieces passing by the right line LAC: which playnes let be ABCD∣L and ACEL, which let cut the playne GCI by the right lines GCH and KCI. Now it is manifest (by the assumpt put before the 17. of this booke) that the two sections of the sphere shall be circles, hauing to their diameter the line LAC, which is also the diameter of the sphere. Wherefore the right lines GCH and KCI which are drawne in the playne GCI, do at the poynt C fall without the circles BCDL and ECL. Wherefore they touch the circles in the poynt C, by the second definition of the third. Wherefore the right line LAC maketh right angles with the lines GCH and KCI by the 16. of the third. Wherefore by the 4. of the eleuenth the right line AC is erected perpendicularly to to the playne superficies GCI wherein are drawne the lines GCH and KCI. If therefore a Sphere touch a playne superficies, a right line drawne from the centre to the touche, shall be erected perpendi∣cularly to the playne superficies: which was required to be proued.