Elements of Geometry and Trigonometry |
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Page 3
In the original work , as well as in the translations of Dr. Brewster and Professor Farrar , the propositions are not enunciated in general terms , but with reference to , and by the aid of , the particular diagrams used for the ...
In the original work , as well as in the translations of Dr. Brewster and Professor Farrar , the propositions are not enunciated in general terms , but with reference to , and by the aid of , the particular diagrams used for the ...
Page 4
Besides the alterations in the enunciation of tivo propositions , others of considerable importance havo also been made in the present edition . The proposition in Book V. , which proves that a polygon and circle may be made to coincide ...
Besides the alterations in the enunciation of tivo propositions , others of considerable importance havo also been made in the present edition . The proposition in Book V. , which proves that a polygon and circle may be made to coincide ...
Page 12
An axiom is a self - evident proposition . ... The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions .
An axiom is a self - evident proposition . ... The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions .
Page 14
PROPOSITION I. THEOREM . - A B . a If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight E ! line AB at C , then will the ...
PROPOSITION I. THEOREM . - A B . a If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight E ! line AB at C , then will the ...
Page 15
PROPOSITION III . THEOREM . -В If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same ...
PROPOSITION III . THEOREM . -В If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same ...
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Common terms and phrases
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 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 number of sides oblique lines opposite parallel 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 S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM trian triangle ABC triangular prism vertex
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 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.
Page 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'.
Page 168 - 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.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.