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 12
... equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to the whole angle BGC . Since , then , the two ...
... equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to the whole angle BGC . Since , then , the two ...
Página 13
... equal to two right an- gles therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater ...
... equal to two right an- gles therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater ...
Página 15
... equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the angle ABD is like- wise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . B PROP . XII . THEOR . The greater ...
... equal ( 3. 1. ) to ABD , be- cause the side AB is equal to the side . AD ; therefore the angle ABD is like- wise greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB . B PROP . XII . THEOR . The greater ...
Página 17
... equal to the angle BAC : and make DG equal to AC or DF , 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 ...
... equal to the angle BAC : and make DG equal to AC or DF , 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 ...
Página 18
... equal . For the side AB is common to the two tri- angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as ...
... equal . For the side AB is common to the two tri- angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as ...
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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