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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
Dentro del libro
Resultados 6-10 de 100
Página 13
... angles with the straight line CBE , upon one side of it , the angles ABC , ABE are to- gether equal ( 6. 1. ) to two right an- gles ; but the angles ABC , ABD are likewise together equal to two right an- gles therefore the angles CBA , ABE ...
... angles with the straight line CBE , upon one side of it , the angles ABC , ABE are to- gether equal ( 6. 1. ) to two right an- gles ; but the angles ABC , ABD are likewise together equal to two right an- gles therefore the angles CBA , ABE ...
Página 14
... equal to BE ; join also FC , and produce AC to G. A F 4 B E D Because AE is equal to EC , and BE to EF ; AE , EB are ... angles to the remaining angles each to each , to which the equal sides are opposite ; wherefore the angle BAE is ...
... equal to BE ; join also FC , and produce AC to G. A F 4 B E D Because AE is equal to EC , and BE to EF ; AE , EB are ... angles to the remaining angles each to each , to which the equal sides are opposite ; wherefore the angle BAE is ...
Página 18
... equal distances on the other line , will be equal ; and any two other oblique lines , cutting off unequal distances ... angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence ...
... equal distances on the other line , will be equal ; and any two other oblique lines , cutting off unequal distances ... angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence ...
Página 19
... angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ... angle EGB is equal to the angle GHD OF GEOMETRY . BOOK I. 19.
... angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ... angle EGB is equal to the angle GHD OF GEOMETRY . BOOK I. 19.
Página 20
... equal to the angle GHD ; and they are the alternate angles ; therefore AB is parallel ( 19. 1. ) to CD . Again , because the angles BGH , GHD are equal ( by Hyp . ) to two right angles , and AGH , BGH , are also equal ( 6. 1. ) to two ...
... equal to the angle GHD ; and they are the alternate angles ; therefore AB is parallel ( 19. 1. ) to CD . Again , because the angles BGH , GHD are equal ( by Hyp . ) to two right angles , and AGH , BGH , are also equal ( 6. 1. ) to two ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore