Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1866 - 317 Seiten |
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Seite 32
... consequently , the op posite sides are parallel ; namely , the side AB parallel to CD , and BD på 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 på rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3. Hence , also , if the opposite angles of a quadrilateral be ...
Seite 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 ...
Seite 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 ...
Seite 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 ...
Seite 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- A F E dicular ...
... 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- A F E dicular ...
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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 Let the straight 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 spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore