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 sider |
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Side 131
... polygons have ; and the polygon ABCDE has to the poly- gon FGHKL a ratio duplicate of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is ...
... polygons have ; and the polygon ABCDE has to the poly- gon FGHKL a ratio duplicate of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is ...
Side 132
... polygon ABCDE to the polygon FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homologous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
... polygon ABCDE to the polygon FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homologous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
Side 133
... polygons are composed of the same number of triangles similar , and similarly situated , those two polygons will be similar . For the similarity of the two triangles will give the angles EAB = LFG , ABE FGL , EBC = LGH : hence , ABC ...
... polygons are composed of the same number of triangles similar , and similarly situated , those two polygons will be similar . For the similarity of the two triangles will give the angles EAB = LFG , ABE FGL , EBC = LGH : hence , ABC ...
Side 157
... be shorter than APDQB . But , by hypothesis , this latter was shorter than any other ; hence that hypothesis was false ; hence all of the enveloping lines are longer than AMB . COR . 1. Hence the perimeter of any polygon inscribed.
... be shorter than APDQB . But , by hypothesis , this latter was shorter than any other ; hence that hypothesis was false ; hence all of the enveloping lines are longer than AMB . COR . 1. Hence the perimeter of any polygon inscribed.
Side 158
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawn , touching a circle , these two lines are together greater than the arc intercepted between them ; and ...
... polygon inscribed in a circle is less than the circumference of the circle . COR . 2. If from a point two straight lines be drawn , touching a circle , these two lines are together greater than the arc intercepted between them ; and ...
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Vanlige uttrykk og setninger
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