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 13
... half of the angle A. The square of the line AB is designated by AB ' ; its cube by AB . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means ...
... half of the angle A. The square of the line AB is designated by AB ' ; its cube by AB . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means ...
Σελίδα 23
... half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side ...
... half of ABF , is shorter than AC , the half of ACF ; hence , the per- pendicular is shorter than any oblique line . Secondly . Let us suppose BC = BE ; then will the triangle CAB be equal to the the triangle BAE ; for BC = BE , the side ...
Σελίδα 47
... half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . F K H Secondly Let ...
... half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop . XVII . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . F K H Secondly Let ...
Σελίδα 54
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD ...
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD ...
Σελίδα 55
... half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference BOD , that is , by the fourth part of the whole cir- cumference . Cor . 3. Every ...
... half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference BOD , that is , by the fourth part of the whole cir- cumference . Cor . 3. Every ...
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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...