Elements of Geometry and Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1869 - 382 pages |
From inside the book
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Page 13
... drawn from one point to another . 11. From one point to another only one straight line can be drawn . 12. Through the same point only one parallel to a straight line can be drawn . 13. All right angles are equal to one another . 2 BOOK I.
... drawn from one point to another . 11. From one point to another only one straight line can be drawn . 12. Through the same point only one parallel to a straight line can be drawn . 13. All right angles are equal to one another . 2 BOOK I.
Page 14
... drawn through a given point parallel to another straight line . 4. That a perpendicular to a given straight line may be drawn from a point either within or without the line . 5. That an angle may be described equal to any given angle ...
... drawn through a given point parallel to another straight line . 4. That a perpendicular to a given straight line may be drawn from a point either within or without the line . 5. That an angle may be described equal to any given angle ...
Page 20
... draw CD . Now , in the two triangles DBC , ABC , we have D B equal to AC by construction , the side BC common , and the angle B equal to the angle ACB by hypothesis ; therefore , since two sides and the included angle in the one are ...
... draw CD . Now , in the two triangles DBC , ABC , we have D B equal to AC by construction , the side BC common , and the angle B equal to the angle ACB by hypothesis ; therefore , since two sides and the included angle in the one are ...
Page 21
... drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side A B is less than the sum of the sides AC ... Draw the straight line CD , making the angle B C D equal to B. Then , in c the triangle BD C , we shall have the B ...
... drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side A B is less than the sum of the sides AC ... Draw the straight line CD , making the angle B C D equal to B. Then , in c the triangle BD C , we shall have the B ...
Page 23
... drawn to that line . Let A be the point , and DE the given straight line ; then from the point A only one perpendicular can be drawn to DE . Let it be supposed that we can draw two perpendiculars , AB and AC . Produce one of them , as ...
... drawn to that line . Let A be the point , and DE the given straight line ; then from the point A only one perpendicular can be drawn to DE . Let it be supposed that we can draw two perpendiculars , AB and AC . Produce one of them , as ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle equal angles ACD base bisect centre chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater GREENLEAF'S half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent triangle ABC triangle equal trigonometric functions TRIGONOMETRY vertex
Popular passages
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 95 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 172 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their common section, will be perpendicular to the other plane.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 94 - In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals.
Page 102 - 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'.