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 30
... divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A ...
... divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general , into as many triangles , less two , as the polygon has sides ; for , these triangles may be considered as having the point A ...
Seite 34
... divided into M number of units , each equal to A ' : then AMX A ' : let B be divided into N number of equal units , each equal to A ' ; then B = Nx A ' ; M and N being integral num- bers . Now the ratio of A to B , will be the same as ...
... divided into M number of units , each equal to A ' : then AMX A ' : let B be divided into N number of equal units , each equal to A ' ; then B = Nx A ' ; M and N being integral num- bers . Now the ratio of A to B , will be the same as ...
Seite 35
... same ratio as the other diminishes . In such case , either of them is equal to a constant quantity divided by the other , and their product is constant . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35.
... same ratio as the other diminishes . In such case , either of them is equal to a constant quantity divided by the other , and their product is constant . PROPOSITION I. THEOREM . When four quantities are in proportion BOOK II . 35.
Seite 52
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the partial arcs Dr , xy , & c . ( Prop . XV . ) . Therefore the whole arc ...
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the partial arcs Dr , xy , & c . ( Prop . XV . ) . Therefore the whole arc ...
Seite 53
... divided into equal parts , each of which is less than DO ; there will be at least one point of division between D and O ; let I be that point ; and draw CI . The arcs AB , AI , will be to each other as two whole numbers , and by the ...
... divided into equal parts , each of which is less than DO ; there will be at least one point of division between D and O ; let I be that point ; and draw CI . The arcs AB , AI , will be to each other as two whole numbers , and by 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...