Elements of Geometry: With Practical Applications to Mensuration |
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Page 3
... propositions . In almost all cases where it was possible , the converse of a proposition has been demonstrated . The demonstration of Proposition XX . of the first book is essentially the one given by M. da Cunha in the Principes Mathé ...
... propositions . In almost all cases where it was possible , the converse of a proposition has been demonstrated . The demonstration of Proposition XX . of the first book is essentially the one given by M. da Cunha in the Principes Mathé ...
Page 14
... proposition preparatory to the dem- onstration or solution of a succeeding proposition . 41. A COROLLARY is an obvious consequence deduced from one or more propositions . . 42. A SCHOLIUM is a remark made upon one or more preceding ...
... proposition preparatory to the dem- onstration or solution of a succeeding proposition . 41. A COROLLARY is an obvious consequence deduced from one or more propositions . . 42. A SCHOLIUM is a remark made upon one or more preceding ...
Page 15
With Practical Applications to Mensuration Benjamin Greenleaf. enunciation of a proposition , or in the course of a demon- stration . PROPOSITION I.THEOREM . 44. The adjacent angles which one straight line makes by meeting another ...
With Practical Applications to Mensuration Benjamin Greenleaf. enunciation of a proposition , or in the course of a demon- stration . PROPOSITION I.THEOREM . 44. The adjacent angles which one straight line makes by meeting another ...
Page 18
... PROPOSITION V. - THEOREM . A D 52. If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other , each to each , the two triangles will be equal . In the two triangles ABC ...
... PROPOSITION V. - THEOREM . A D 52. If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other , each to each , the two triangles will be equal . In the two triangles ABC ...
Page 21
... PROPOSITION IX . THEOREM . - 62. Any side of a triangle is less than the sum of the other two . In the triangle ABC , any one side , as A B , is less than the sum of the other two sides , A C and C B. A C B For the straight line AB is ...
... PROPOSITION IX . THEOREM . - 62. Any side of a triangle is less than the sum of the other two . In the triangle ABC , any one side , as A B , is less than the sum of the other two sides , A C and C B. A C B For the straight line AB is ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect 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 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 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 THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
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 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
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 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 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.