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 4
... segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one ...
... segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one ...
Página 45
... segments AC , CB , by b and d , respectively ; then , a = b + d ; therefore , multiplying both members of this equality by a , we shall have a2 = ab + ad . PROP . III . THEOR . If a straight line OF GEOMETRY . BOOK II . 45.
... segments AC , CB , by b and d , respectively ; then , a = b + d ; therefore , multiplying both members of this equality by a , we shall have a2 = ab + ad . PROP . III . THEOR . If a straight line OF GEOMETRY . BOOK II . 45.
Página 46
... segments AC and CB , by b and c ; then a = b + c : therefore , multiplying both members of this equality by c , we shall have ac = bc + c2 . PROP . IV . THEOR . If a straight line be divided into any two parts , the square of the whole ...
... segments AC and CB , by b and c ; then a = b + c : therefore , multiplying both members of this equality by c , we shall have ac = bc + c2 . PROP . IV . THEOR . If a straight line be divided into any two parts , the square of the whole ...
Página 49
... segments AC and CB by b and c ; then a2b2 + 26c + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2b2 + 2bc + 2c2 ; ..a2 + c2 = b2 + 2c ( b + c ) , or a2 + c2 = 2ac + b2 . COR . From this proposition it is evident ...
... segments AC and CB by b and c ; then a2b2 + 26c + c2 ; adding c2 to each member of this equality , we shall have , a2 + c2b2 + 2bc + 2c2 ; ..a2 + c2 = b2 + 2c ( b + c ) , or a2 + c2 = 2ac + b2 . COR . From this proposition it is evident ...
Página 55
... segment of a circle is the figure con- tained by a straight line , and the arc which it cuts off . 9. An angle in a segment is the angle contained.
... segment of a circle is the figure con- tained by a straight line , and the arc which it cuts off . 9. An angle in a segment is the angle contained.
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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