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 10
... difference of the two A angles DCE , BCE . 10. When a straight line AB meets another straight line CD , so as to make the adjacent angles BAC , BAD , equal to each other , each of these angles is called a right angle ; and the line AB ...
... difference of the two A angles DCE , BCE . 10. When a straight line AB meets another straight line CD , so as to make the adjacent angles BAC , BAD , equal to each other , each of these angles is called a right angle ; and the line AB ...
Σελίδα 12
... difference , or what remains after B is taken from A ; and A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum . The sign indicates multiplication : thus , A × B 12 ...
... difference , or what remains after B is taken from A ; and A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum . The sign indicates multiplication : thus , A × B 12 ...
Σελίδα 34
... difference . Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the whole , and one of those parts being considered as an unit of measure , the magnitude may ...
... difference . Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the whole , and one of those parts being considered as an unit of measure , the magnitude may ...
Σελίδα 35
... difference of the antecedent and consequent is compared either with antecedent or consequent . 9. Equimultiples of two quantities are the products which arise from multiplying the quantities by the same number : thus , m × A , m × B ...
... difference of the antecedent and consequent is compared either with antecedent or consequent . 9. Equimultiples of two quantities are the products which arise from multiplying the quantities by the same number : thus , m × A , m × B ...
Σελίδα 50
... difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis- tance from each other equal to AD - CA . It is evident , as before , that they will have the point A common ; they can ...
... difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis- tance from each other equal to AD - CA . It is evident , as before , that they will have the point A common ; they can ...
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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...