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 |
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Página 15
... ABC greater than ACB . B PROP . XII . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the an- gle BCA ...
... ABC greater than ACB . B PROP . XII . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the an- gle BCA ...
Página 16
... triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 13. 1. ) are ...
... triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 13. 1. ) are ...
Página 18
... ABC . But the less angle of a triangle is subtended by the less side ( Th . 12. ) ; therefore , the side AB is less ... ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC ...
... ABC . But the less angle of a triangle is subtended by the less side ( Th . 12. ) ; therefore , the side AB is less ... ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC ...
Página 19
... triangles ABC and DEF are equal . PROP . XIX . THEOR . If a straight line falling upon two other straight lines ... triangle , and its exterior angle AEF is greater ( 9. 1. ) than the interior and opposite angle EFG ; but it is also ...
... triangles ABC and DEF are equal . PROP . XIX . THEOR . If a straight line falling upon two other straight lines ... triangle , and its exterior angle AEF is greater ( 9. 1. ) than the interior and opposite angle EFG ; but it is also ...
Página 22
... ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of the triangle , viz . ABC , BČA , CAB , are together ...
... ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of the triangle , viz . ABC , BČA , CAB , are together ...
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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