The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfthA. Foulis, 1781 - 466 pàgines |
Des de l'interior del llibre
Resultats 1 - 5 de 100.
Pàgina 15
... Manner Corrected. viz. The first six books, together with the eleventh and t Robert Simson. angle CBE is equal to the angle EBA ; in the fame manner , because ABD is a straight line , the angle DBE is equal to the angle EBA . wherefore ...
... Manner Corrected. viz. The first six books, together with the eleventh and t Robert Simson. angle CBE is equal to the angle EBA ; in the fame manner , because ABD is a straight line , the angle DBE is equal to the angle EBA . wherefore ...
Pàgina 17
... fame straight line with BC . And in like manner , it may be demonftrated that no other can be in the fame ftraight line with it but BD , which therefore is in the fame ftraight line with CB . Wherefore if at a point , & c . Q. E. D. b ...
... fame straight line with BC . And in like manner , it may be demonftrated that no other can be in the fame ftraight line with it but BD , which therefore is in the fame ftraight line with CB . Wherefore if at a point , & c . Q. E. D. b ...
Pàgina 18
... fame manner , if the fide BC be bifected , it may be demonftrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . therefore if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angls of a triangle ...
... fame manner , if the fide BC be bifected , it may be demonftrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . therefore if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angls of a triangle ...
Pàgina 20
... fame manner it may be demonstrated that the fides AB , BC are greater than CA ; and BC , CA greater than AB . therefore any two fides , & c . Q. E. D. IF PROP . XXI . THEOR . F from the ends of the fide of a triangle there be drawn two ...
... fame manner it may be demonstrated that the fides AB , BC are greater than CA ; and BC , CA greater than AB . therefore any two fides , & c . Q. E. D. IF PROP . XXI . THEOR . F from the ends of the fide of a triangle there be drawn two ...
Pàgina 32
... Manner Corrected. viz. The first six books, together with the eleventh and t Robert Simson. c Book I. angle BCD ... fame parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the fame base BC and between the ...
... Manner Corrected. viz. The first six books, together with the eleventh and t Robert Simson. c Book I. angle BCD ... fame parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the fame base BC and between the ...
Altres edicions - Mostra-ho tot
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Visualització completa - 1775 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Visualització completa - 1762 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Visualització completa - 1827 |
Frases i termes més freqüents
AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore
Passatges populars
Pàgina 156 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Pàgina 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Pàgina 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Pàgina 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Pàgina 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Pàgina 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Pàgina 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pàgina 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Pàgina 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Pàgina 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...