The Geometrical Companion, in which the Elements of Abstract Geometry are Familiarised, Illustrated, and Rendered Practically Useful, Etc |
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Page 127
... equiangular parallelograms which have the sides about their equal angles reciprocally proportional , are equal . " Here is another criterion of equality between parallelo- grammatic figures . If they be equiangular , and if the sides ...
... equiangular parallelograms which have the sides about their equal angles reciprocally proportional , are equal . " Here is another criterion of equality between parallelo- grammatic figures . If they be equiangular , and if the sides ...
Page 128
... equiangular parallelograms , they must be equal , by ART . 97 , as their sides are reciprocally proportional ... equiangular parallelograms . For we have only to compare , in the manner above shown , each couple of parallelograms . But ...
... equiangular parallelograms , they must be equal , by ART . 97 , as their sides are reciprocally proportional ... equiangular parallelograms . For we have only to compare , in the manner above shown , each couple of parallelograms . But ...
Page 136
... equiangular ( the angles at B and b being both right , and the rays AC , ac , of the sun falling with the same inclination ACB , acb , on the ground ) . Thus , if the pole be 6 feet above the ground , while the length of the shadow is 2 ...
... equiangular ( the angles at B and b being both right , and the rays AC , ac , of the sun falling with the same inclination ACB , acb , on the ground ) . Thus , if the pole be 6 feet above the ground , while the length of the shadow is 2 ...
Page 139
... We have proceeded according to PROB . XX . , for ob- taining a mean proportional between CB and CE , or CB and CD . This mean is cr ; and by ART . 102 , the square of cr is equal to Again : The triangles afb , mfb , being equiangular 139.
... We have proceeded according to PROB . XX . , for ob- taining a mean proportional between CB and CE , or CB and CD . This mean is cr ; and by ART . 102 , the square of cr is equal to Again : The triangles afb , mfb , being equiangular 139.
Page 140
George Darley. Again : The triangles afb , mfb , being equiangular , fa has the same ratio to fm as ab has to mn , and as ae has to mq . Wherefore ab has the same ratio to mn as ae has to mq . In like manner , it may be shown that bc has ...
George Darley. Again : The triangles afb , mfb , being equiangular , fa has the same ratio to fm as ab has to mn , and as ae has to mq . Wherefore ab has the same ratio to mn as ae has to mq . In like manner , it may be shown that bc has ...
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Common terms and phrases
ABCD abstract Art adjacent angles adjacent sides altitude angle BAC Astronomy base bevel blade breadth bricks centre chord circle circular arch circumference Consequently construction corresponding sides curve describe the circular diagonal diameter distance divided draw drawn edge equiangular equilateral triangle Euclid's Elements exactly equal example feet former Geometry given point given right line gonal greater half a right height Hence inches instrument internal angles joining latter LEARNER lelogram length likewise linear unit manner measure method middle point number of equal observed pair parallel parallelogram perpendicular pieces practical PROB problem Pythagoras radius ratio rectangle rectangular rectilineal figure rendered respectively equal right angles right line intersect round square square-feet square-inches square-yards straight line suppose surface tangent TEACHER Thales theorem tremity triangle ABC triangular upright utility vertex wheel whole yards
Popular passages
Page 13 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 106 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 67 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Page 66 - If two triangles have two angles of the one equal respectively to two angles of the other, the third angles are equal.
Page 160 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Page 87 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...
Page 23 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 129 - FGL have an angle in one equal to an angle in the other, and their...
Page 120 - There are two Causes of Beauty, natural and customary. Natural is from Geometry, consisting in Uniformity (that is Equality) and Proportion. Customary Beauty is begotten by the Use of our Senses to those Objects which are usually pleasing to us for other Causes, as Familiarity or particular Inclination breeds a Love to Things not in themselves lovely. Here lies the great Occasion of Errors; here is tried the Architect's Judgment: but always the true Test is natural or geometrical Beauty.
Page 120 - Beauty is a harmony of objects, begetting pleasure by the eye. There are two causes of beauty, natural and customary. Natural is from GEOMETRY, consisting in uniformity (that is, equality) and proportion. Customary beauty is begotten by the use of our senses...