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 Seiten |
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Seite 4
... table of logarithms and logarithmic sines , and to apply the principles of geometry to the mensuration of sur- faces and solids . Military Academy , West Point , March , 1834 . CONTENTS . BOOK I. The principles , BOOK II . iv PREFACE .
... table of logarithms and logarithmic sines , and to apply the principles of geometry to the mensuration of sur- faces and solids . Military Academy , West Point , March , 1834 . CONTENTS . BOOK I. The principles , BOOK II . iv PREFACE .
Seite 127
... face , and ascertain if it touches the surface throughout its whole extent . PROPOSITION II . THEOREM . Two straight lines , which intersect each other , lie in the same plane , and determine its position . Let AB , AC , be two straight ...
... face , and ascertain if it touches the surface throughout its whole extent . PROPOSITION II . THEOREM . Two straight lines , which intersect each other , lie in the same plane , and determine its position . Let AB , AC , be two straight ...
Seite 139
... face produced can ever meet the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude . PROPOSITION XXI . THEOREM . If two solid angles are contained by three plane ...
... face produced can ever meet the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude . PROPOSITION XXI . THEOREM . If two solid angles are contained by three plane ...
Seite 142
... faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a polyedron is called the side , or edge of the polyedron . 3. The prism is a solid bounded by ...
... faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a polyedron is called the side , or edge of the polyedron . 3. The prism is a solid bounded by ...
Seite 143
... faces are rectangles . 9. Among rectangular parallelopipedons , we distinguish the cube , or regular hexaedron ... face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the ...
... faces are rectangles . 9. Among rectangular parallelopipedons , we distinguish the cube , or regular hexaedron ... face . 11. If from the pyramid S - ABCDE , the pyramid S - abcde be cut off by a plane parallel to the base , the ...
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Häufige Begriffe und Wortgruppen
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
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Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 169 - THEOREM. 7?/6 convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
Seite 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.
Seite 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.
Seite 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'.
Seite 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.
Seite 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...