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, 1840 - 317 σελίδες |
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Σελίδα 32
... 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 ...
Σελίδα 42
... consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater angle ( 19. 1. ) ; 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 ( 19. 1. ) ; therefore the side AD is greater than the side AC . COR . 1. The perpendicular measures the true ...
Σελίδα 43
... consequently AH - DF . Now ( by hyp . ) , we have DF = AC ; and therefore , AH - AC . But by the last prop- osition , the oblique line AC can- not be equal to the oblique line AH , which lies nearer to the per- pendicular AB ; therefore ...
... consequently AH - DF . Now ( by hyp . ) , we have DF = AC ; and therefore , AH - AC . But by the last prop- osition , the oblique line AC can- not be equal to the oblique line AH , which lies nearer to the per- pendicular AB ; therefore ...
Σελίδα 86
... consequently divides the circle into two equal parts ; hence the portion AEF is equal to the portion AEFB , which is absurd . COR . The arc of a circle whose chord is a diameter , is a semicircum- ference , and the included segment is a ...
... consequently divides the circle into two equal parts ; hence the portion AEF is equal to the portion AEFB , which is absurd . COR . The arc of a circle whose chord is a diameter , is a semicircum- ference , and the included segment is a ...
Σελίδα 87
... consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpen- B ધ F C ...
... consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides this , no other circumference can pass through the same points ; for the centre , lying in the perpen- B ધ F C ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore