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 Sperical Trigonometry |
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Page 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 ...
Page 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 ...
Page 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 pa- rallel to AC ; and , therefore , the figure is a parallelogram ...
... 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 pa- rallel to AC ; and , therefore , the figure is a parallelogram ...
Page 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 ...
... 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 ...
Page 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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Common terms and phrases
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 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 68 - THE angles in the same segment of a circle are equal to one another...
Page 23 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Page 74 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 78 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 9 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Page 75 - If a straight line touch a circle, and from the point of contact a...
Page 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Page 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.