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 sider |
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Resultat 1-5 av 43
Side 10
... consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it may be inferred that the other ...
... consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it may be inferred that the other ...
Side 18
... consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater angle ( Th . 12. ) ; therefore , the side AD is greater than the side AC . COR . 1. The perpendicular measures the true ...
... consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater angle ( Th . 12. ) ; therefore , the side AD is greater than the side AC . COR . 1. The perpendicular measures the true ...
Side 19
... 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 , which lies A nearer to the perpendicular AB ; B therefore ...
... 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 , which lies A nearer to the perpendicular AB ; B therefore ...
Side 22
... consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I H D B The restriction of this proposition to the case where the side ...
... consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I H D B The restriction of this proposition to the case where the side ...
Side 25
... consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3. Hence , also , if the opposite angles of a quadrilateral be ...
... consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3. Hence , also , if the opposite angles of a quadrilateral be ...
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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