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 15
... THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the an- gle BCA ; the side AČ is likewise greater ...
... THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the an- gle BCA ; the side AČ is likewise greater ...
Página 16
... THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the ...
... THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the ...
Página 17
... THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of the one greater than the base of the other ; the an- gle contained by the sides of that which has the greater base ...
... THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of the one greater than the base of the other ; the an- gle contained by the sides of that which has the greater base ...
Página 18
... THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on different sides of the perpendicular , cutting off ...
... THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on different sides of the perpendicular , cutting off ...
Página 19
... THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make ...
... THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make ...
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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