Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1849 - 359 σελίδες |
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Σελίδα 53
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
Σελίδα 68
... similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
... similar figures , are called homologous sides or angles . A 3. In two different circles , similar arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the arc ...
Σελίδα 73
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
... similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that of the rectangles , agreeably to the proposition just demonstrated . For ...
Σελίδα 84
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED . are two similar figures . Cor . For the similarity of two triangles ...
... similar when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED . are two similar figures . Cor . For the similarity of two triangles ...
Σελίδα 85
... similar triangles , the homolo gous sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC ...
... similar triangles , the homolo gous sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the equal angles ABC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 251 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Σελίδα 109 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV.
Σελίδα 91 - Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E.
Σελίδα 169 - THEOREM. 7?/6 convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
Σελίδα 41 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 155 - AK. The two solids AG, AQ, having the same base AEHD are to each other as their altitudes AB, AO ; in like manner, the two solids AQ, AK, having the same base AOLE, are to each other as their altitudes AD, AM. Hence we have the two proportions, sol.
Σελίδα 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 282 - ... 1. To find the length of an arc of 30 degrees, the diameter being 18 feet. ' Ans. 4.712364. 2. To find the length of an arc of 12° 10', or 12£°, the diameter being 20 feet.
Σελίδα 93 - ABC : FGH : : ACD : FHI. By the same mode of reasoning, we should find ACD : FHI : : ADE : FIK; and so on, if there were more triangles. And from this series of equal ratios, we conclude that the sum of the antecedents...