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
... hence the sum of the two angles DBA and ABC is equal to two right angles . COR . The sum of all the angles , formed on the same side of a straight line DC , is equal to two right angles ; because their sum is equal to that of the two ...
... hence the sum of the two angles DBA and ABC is equal to two right angles . COR . The sum of all the angles , formed on the same side of a straight line DC , is equal to two right angles ; because their sum is equal to that of the two ...
Página 13
... hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . IX . THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the ...
... hence , all the angles made by any number of straight lines meeting in one point , are together equal to four right angles . PROP . IX . THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the ...
Página 18
... hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as before , the adjacent angle ACD will be obtuse ; since ( Th . 6. ) these two angles are together equal to two right angles ; and the angle ADC is acute , because ...
... hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as before , the adjacent angle ACD will be obtuse ; since ( Th . 6. ) these two angles are together equal to two right angles ; and the angle ADC is acute , because ...
Página 19
... hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and therefore , AH = AC . But by the last proposition , the ob- lique line AC cannot be equal to the oblique line AH ...
... hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and therefore , AH = AC . But by the last proposition , the ob- lique line AC cannot be equal to the oblique line AH ...
Página 20
... Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ...
... Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ...
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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