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 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 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 ...
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 plane 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 third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 49 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 147 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 292 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 7 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Page 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...
Page 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Page 78 - 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.