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 31
... wherefore the square upon the side BC is equal to the squares upon the sides BA , AC . COR . 1. Hence , the square of one of the sides of a right angled triangle is equivalent to the square of the hypotenuse diminished by the square of ...
... wherefore the square upon the side BC is equal to the squares upon the sides BA , AC . COR . 1. Hence , the square of one of the sides of a right angled triangle is equivalent to the square of the hypotenuse diminished by the square of ...
Página 33
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn ...
Página 34
... . def . ) angle ; therefore each of the angles DCF , ECF , is a right angle . Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . PROP . VII . PROB . To draw a straight 34 ELEMENTS.
... . def . ) angle ; therefore each of the angles DCF , ECF , is a right angle . Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . PROP . VII . PROB . To draw a straight 34 ELEMENTS.
Página 39
... Wherefore there has been described a parallelogram FECG equal to a given triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle ...
... Wherefore there has been described a parallelogram FECG equal to a given triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle ...
Página 40
... wherefore LB is equal to the triangle C ; and because the angle GBE is equal ( 8. 1. ) to the angle ABM , and likewise to the angle D ; the angle ABM is equal to the angle D : Therefore the parallelogram LB , which is applied to the ...
... wherefore LB is equal to the triangle C ; and because the angle GBE is equal ( 8. 1. ) to the angle ABM , and likewise to the angle D ; the angle ABM is equal to the angle D : Therefore the parallelogram LB , which is applied to the ...
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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