Elements of Plane and Spherical Trigonometry: With Practical ApplicationsR. S. Davis, 1862 - 490 páginas |
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Página 14
... propositions . 42. A SCHOLIUM is a remark made upon one or more preceding propositions . 43. An HYPOTHESIS is a supposition , made either in the enunciation of a proposition , or in the course of 14 ELEMENTS OF GEOMETRY .
... propositions . 42. A SCHOLIUM is a remark made upon one or more preceding propositions . 43. An HYPOTHESIS is a supposition , made either in the enunciation of a proposition , or in the course of 14 ELEMENTS OF GEOMETRY .
Página 29
... Scholium . In two triangles equal to each other , the equal angles are opposite the equal sides ; thus the equal angles A and D are opposite the equal sides B C and EF . PROPOSITION XIX . - THEOREM . 82. If two right - angled triangles ...
... Scholium . In two triangles equal to each other , the equal angles are opposite the equal sides ; thus the equal angles A and D are opposite the equal sides B C and EF . PROPOSITION XIX . - THEOREM . 82. If two right - angled triangles ...
Página 34
... Scholium . The two lines K L , CD , on being pro- duced , must meet on the side of E F , on which are the two interior angles whose sum is less than two right angles . PROPOSITION XXIV . - THEOREM . 90. Straight lines which are parallel ...
... Scholium . The two lines K L , CD , on being pro- duced , must meet on the side of E F , on which are the two interior angles whose sum is less than two right angles . PROPOSITION XXIV . - THEOREM . 90. Straight lines which are parallel ...
Página 35
... Scholium . This proposition is restricted to the case where the side EF lies in the same direction with BC , since if FE were produced toward H , the angles DEH , ABC would only be equal when they are right angles . PROPOSITION XXVII ...
... Scholium . This proposition is restricted to the case where the side EF lies in the same direction with BC , since if FE were produced toward H , the angles DEH , ABC would only be equal when they are right angles . PROPOSITION XXVII ...
Página 38
... Scholium . In applying this prop- osition to polygons which have re - en- trant angles , or angles whose vertices are directed inward , as BP C , each of these angles must be considered greater than two right angles . But , in order to ...
... Scholium . In applying this prop- osition to polygons which have re - en- trant angles , or angles whose vertices are directed inward , as BP C , each of these angles must be considered greater than two right angles . But , in order to ...
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Términos y frases comunes
A B C ABCD adjacent angles altitude angle ACB angle equal 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 half the sum hence homologous hypothenuse inches included angle inscribed interior angles 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 Required the area 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
Pasajes populares
Página 28 - 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.
Página 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.
Página 79 - Two rectangles having equal altitudes are to each other as their bases.
Página 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Página 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.
Página 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.
Página 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Página 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Página 4 - 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. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Página 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.