The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh and Twelfth. 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 CorrE. Wingrove, London, and J. Balfour, Edinburgh, 1793 - 520 páginas |
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Página 39
... parallelograms are equal to one another , and the diameter bifects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opponite fides and angles of the figure are equal to one a- nother ...
... parallelograms are equal to one another , and the diameter bifects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opponite fides and angles of the figure are equal to one a- nother ...
Página 40
... parallelograms ABCD . EBCF , be not terminated in the fame point ; then , be- . cause ABCD is a parallelogram , AD is equal a to BC ; for the fame reafon EF is equal to BC ; wherefore AD is equal b to EF ; and DE is common ; therefore ...
... parallelograms ABCD . EBCF , be not terminated in the fame point ; then , be- . cause ABCD is a parallelogram , AD is equal a to BC ; for the fame reafon EF is equal to BC ; wherefore AD is equal b to EF ; and DE is common ; therefore ...
Página 42
... parallelogram DBCF , because the diameter DC bifects it : But the halves of equal things are e- qual d ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. TR PROP . XXXVIII . THEOR ...
... parallelogram DBCF , because the diameter DC bifects it : But the halves of equal things are e- qual d ; therefore the triangle ABC is equal to the triangle DBC . Wherefore triangles , & c . Q. E. D. TR PROP . XXXVIII . THEOR ...
Página 43
... Q. E. D. IF PROP . XLI . THEOR . F a parallelogram and triangle be upon the fame bafe , and between the fame parallels ; the paral- lelogram fhall be double of the triangle . Let a 31 . b 38. Ii Book 1 . a 37. I. b 34. I. a OF EUCLID . 43.
... Q. E. D. IF PROP . XLI . THEOR . F a parallelogram and triangle be upon the fame bafe , and between the fame parallels ; the paral- lelogram fhall be double of the triangle . Let a 31 . b 38. Ii Book 1 . a 37. I. b 34. I. a OF EUCLID . 43.
Página 44
... parallelogram ABCD and the triangle EBC be upon tlfe fame base BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . A Join AC ; then the triangle ABC is equal a to the triangle EBC ...
... parallelogram ABCD and the triangle EBC be upon tlfe fame base BC , and between the fame parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . A Join AC ; then the triangle ABC is equal a to the triangle EBC ...
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Otras ediciones - Ver todas
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Vista de fragmentos - 1803 |
Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fide BC fides fimilar 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 parallelepiped parallelogram perpendicular plane angles PROP propofition proportionals pyramid rectangle contained rectilineal figure right angles ſame ſhall ſphere ſquare THEOR theſe tiple triangle ABC wherefore