Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1866 - 317 Seiten |
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Seite 15
... equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ...
... equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ...
Seite 31
... equiangular . COR . 5. In any triangle there can be but one right angle ; for if there were two , the third angle ... equiangular , each angle is equal to the fifth part of six right angles , or of one right angle . COR . 10. The sum of ...
... equiangular . COR . 5. In any triangle there can be but one right angle ; for if there were two , the third angle ... equiangular , each angle is equal to the fifth part of six right angles , or of one right angle . COR . 10. The sum of ...
Seite 32
... equiangular ( Th . 8. ) , or have their corresponding angles equal ; consequently , the op posite sides are parallel ; namely , the side AB parallel to CD , and BD på rallel to AC ; and , therefore , the figure is a parallelogram . COR ...
... equiangular ( Th . 8. ) , or have their corresponding angles equal ; consequently , the op posite sides are parallel ; namely , the side AB parallel to CD , and BD på rallel to AC ; and , therefore , the figure is a parallelogram . COR ...
Seite 92
... equiangular , is called a regular polygon . Regular polygons may have any number of sides ; the equilateral tri angle is one of three sides ; and the square is one of four sides . LEMMA . Any regular polygon may be inscribed in a circle ...
... equiangular , is called a regular polygon . Regular polygons may have any number of sides ; the equilateral tri angle is one of three sides ; and the square is one of four sides . LEMMA . Any regular polygon may be inscribed in a circle ...
Seite 93
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is re- quired to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw ( Prop . 17. 3. ) the straight line GAH ...
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is re- quired to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw ( Prop . 17. 3. ) the straight line GAH ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore