Elements of Geometry and Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1862 - 490 páginas |
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Página 12
With Practical Applications Benjamin Greenleaf. A SQUARE is a rectangle whose sides are equal ; as the rectangle EFGH . 27. A RHOMBOID is any parallelo- gram whose angles are not right an- gles ; as the parallelogram IJKL . A RHOMBUS is ...
With Practical Applications Benjamin Greenleaf. A SQUARE is a rectangle whose sides are equal ; as the rectangle EFGH . 27. A RHOMBOID is any parallelo- gram whose angles are not right an- gles ; as the parallelogram IJKL . A RHOMBUS is ...
Página 48
... square of the mean . Let A B B : C ; then will A X C : = B2 . For , since the magnitudes are in proportion , A B = B C and , by Prop . I. , AX CBX B , or AXC B2 . = PROPOSITION IV . - THEOREM . 138. If the product 48 ELEMENTS OF GEOMETRY .
... square of the mean . Let A B B : C ; then will A X C : = B2 . For , since the magnitudes are in proportion , A B = B C and , by Prop . I. , AX CBX B , or AXC B2 . = PROPOSITION IV . - THEOREM . 138. If the product 48 ELEMENTS OF GEOMETRY .
Página 49
... square of a third , the third is a mean proportional between the other two . Let AXC tween A and C. = B2 ; then B is a mean proportional be- For , dividing each member of the given equation by BX C , we have A B whence = B C A : B :: B ...
... square of a third , the third is a mean proportional between the other two . Let AXC tween A and C. = B2 ; then B is a mean proportional be- For , dividing each member of the given equation by BX C , we have A B whence = B C A : B :: B ...
Página 53
... square of the first is to the square of the second . Let A : B :: B : C ; then will A : C : : A2 : B2 . For , from the given proportion , by Prop . III . , we have АХС : A X CB2 . Multiplying each side of this equation by A gives A2 X ...
... square of the first is to the square of the second . Let A : B :: B : C ; then will A : C : : A2 : B2 . For , from the given proportion , by Prop . III . , we have АХС : A X CB2 . Multiplying each side of this equation by A gives A2 X ...
Página 76
... square , and a tri- angle to a rectangle . 212. EQUAL FIGURES are such as , when applied the one to the other , coincide throughout ( Art . 34 , Ax . 14 ) . Thus circles having equal radii are equal ; and triangles having the three ...
... square , and a tri- angle to a rectangle . 212. EQUAL FIGURES are such as , when applied the one to the other , coincide throughout ( Art . 34 , Ax . 14 ) . Thus circles having equal radii are equal ; and triangles having the three ...
Otras ediciones - Ver todas
Elements of Geometry and Trigonometry: With Practical Applications Benjamin Greenleaf Vista completa - 1869 |
Elements of Geometry and Trigonometry: With Practical Applications Benjamin Greenleaf Vista completa - 1867 |
Términos y frases comunes
A B C ABCD adjacent angles altitude 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 less Let ABC line A B logarithm logarithmic sine mean proportional 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 sine slant height solidity solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Pasajes populares
Página 35 - 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 57 - 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 117 - 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.
Página 50 - If any number of magnitudes 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; then will A : B : : A + C + E : B + D + F.
Página 77 - Two rectangles having equal altitudes are to each other as their bases.
Página 158 - 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 313 - FRACTION is a negative number, and is one more tftan the number of ciphers between the decimal point and the first significant figure.
Página 314 - 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.
Página 100 - 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'.
Página 244 - RULE. — Multiply the base by the altitude, and the product will be the area.