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 TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 11
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
Página 14
... Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. B A E F D Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and ...
... Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. B A E F D Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and ...
Página 15
... join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the ...
... join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the ...
Página 17
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the an- gle BAC is equal to the angle EDG , therefore the base BC is equal ( 1. 1. ) to the base EG ; and ...
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the an- gle BAC is equal to the angle EDG , therefore the base BC is equal ( 1. 1. ) to the base EG ; and ...
Página 18
... , if the third sides BC and EF were equal . If possible , suppose that those sides are not equal , and that BC is the greater . Take BH - EF ; and join AH . The triangle ABH - DEF ; for the right angles B and E are equal , 18 ELEMENTS.
... , if the third sides BC and EF were equal . If possible , suppose that those sides are not equal , and that BC is the greater . Take BH - EF ; and join AH . The triangle ABH - DEF ; for the right angles B and E are equal , 18 ELEMENTS.
Otras ediciones - Ver todas
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
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 draw Prob 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