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 56
... through it , which is therefore a diameter , and 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 56 ELEMENTS.
... through it , which is therefore a diameter , and 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 56 ELEMENTS.
Página 60
... Consequently , that point from which three equal lines can be drawn is the centre . PROP . VIII . THEOR . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the ...
... Consequently , that point from which three equal lines can be drawn is the centre . PROP . VIII . THEOR . If any point be taken without a circle , and straight lines be drawn from it to the circumference , whereof one passes through the ...
Página 63
... consequently the two circles cannot cut each other . PROP . XI . THEOR . If two circles touch each other internally , the straight line which joins their centres being produced , will pass through the point of contact . Let the two ...
... consequently the two circles cannot cut each other . PROP . XI . THEOR . If two circles touch each other internally , the straight line which joins their centres being produced , will pass through the point of contact . Let the two ...
Página 76
... consequently the other two angles , BAD , ABD , are equal ( 25. 1. ) to a right angle ; but ABF is likewise a right angle ; therefore the angle ABF is equal to the angles BAD , ABD take from these equals the com- mon angle ABD , and ...
... consequently the other two angles , BAD , ABD , are equal ( 25. 1. ) to a right angle ; but ABF is likewise a right angle ; therefore the angle ABF is equal to the angles BAD , ABD take from these equals the com- mon angle ABD , and ...
Página 86
... consequently the circle which passes through the three points A , B , C , will also pass through the point D. By the ... consequently , being chords of the circumscribed circle , they are equal , and therefore include equal angles ...
... consequently the circle which passes through the three points A , B , C , will also pass through the point D. By the ... consequently , being chords of the circumscribed circle , they are equal , and therefore include equal angles ...
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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