Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
Dentro del libro
Resultados 6-10 de 48
Página 42
... falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite ...
... falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite ...
Página 49
... falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are less than two right angles : But straight lines which with another straight line make the ...
... falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are less than two right angles : But straight lines which with another straight line make the ...
Página 55
... falls upon them , the exterior an- gle BGC is equal ( 29. 1. ) to the interior and opposite angle ADB ; but ADB is e- qual ( 5. 1 ) to the angle ABD , because BA is equal to AD , being sides of a square ; wherefore the angle CGB is ...
... falls upon them , the exterior an- gle BGC is equal ( 29. 1. ) to the interior and opposite angle ADB ; but ADB is e- qual ( 5. 1 ) to the angle ABD , because BA is equal to AD , being sides of a square ; wherefore the angle CGB is ...
Página 62
... fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1. ) AD from the ...
... fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1. ) AD from the ...
Página 63
... fall without the triangle ABC * : Then because the angle at D is a right angle , the angle ACB is greater ( 16.1 . ) than a right angle , and AB ( 12. 2. ) AČ2 + BC2 + 2BC CD . Add BC2 to each ; then AB2 + BC2AC2 + 2BC2 + 2BC.CD. But ...
... fall without the triangle ABC * : Then because the angle at D is a right angle , the angle ACB is greater ( 16.1 . ) than a right angle , and AB ( 12. 2. ) AČ2 + BC2 + 2BC CD . Add BC2 to each ; then AB2 + BC2AC2 + 2BC2 + 2BC.CD. But ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore