Elements of Geometry and Trigonometry |
From inside the book
Page 40
... proportional , their squares or cubes will also be proportional . Let and then will For since and or N m therefore , PROPOSITION XII . THEOREM . M : NP : Q , M2 : N2 : : P2 : Q2 M3 : N3 P3 : Q3 therefore , M2 : N ° :: P2 : Q ° and M3 ...
... proportional , their squares or cubes will also be proportional . Let and then will For since and or N m therefore , PROPOSITION XII . THEOREM . M : NP : Q , M2 : N2 : : P2 : Q2 M3 : N3 P3 : Q3 therefore , M2 : N ° :: P2 : Q ° and M3 ...
Page 98
... proportionally in C and I ( Prop . XV . ) . But AC is the fifth part of AG , hence AI is the fifth part of AB , D M B Pr Secondly . Let it be proposed to divide the line AB into parts proportional to the given lines P , Q , R. Through A ...
... proportionally in C and I ( Prop . XV . ) . But AC is the fifth part of AG , hence AI is the fifth part of AB , D M B Pr Secondly . Let it be proposed to divide the line AB into parts proportional to the given lines P , Q , R. Through A ...
Page 99
... proportional required . F A E B D PROBLEM III . I PROBLEM IV . A BCICor . A third proportional to two given lines A , B , may be found in the same manner , for it will be the same as a fourth proportional to the three lines A , B , B ...
... proportional required . F A E B D PROBLEM III . I PROBLEM IV . A BCICor . A third proportional to two given lines A , B , may be found in the same manner , for it will be the same as a fourth proportional to the three lines A , B , B ...
Contents
Ratios and Proportions | 34 |
The Circle and the Measurement of Angles | 41 |
Problems relating to the First and Third Books | 57 |
14 other sections not shown
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Common terms and phrases
adjacent adjacent angles 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 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 M.
M. Sine number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism vertex
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |