Elements of Geometry and Trigonometry: With Practical Applications |
From inside the book
Results 1-5 of 7
Page 226
... quadrantal . The quadrantal triangle is evidently contained eight times in the surface of the sphere . PROPOSITION XI . - THEOREM . 545. If around the vertices of any two angles of a given spherical triangle , as poles , the ...
... quadrantal . The quadrantal triangle is evidently contained eight times in the surface of the sphere . PROPOSITION XI . - THEOREM . 545. If around the vertices of any two angles of a given spherical triangle , as poles , the ...
Page 234
... quadrantal triangles ( Prop . X. Sch . ) . Hence , if the area of a quadrantal triangle be represented by T , the surface of the sphere will be repre- sented by 8T . Now , if the right angle be assumed as unity , and the angle of the ...
... quadrantal triangles ( Prop . X. Sch . ) . Hence , if the area of a quadrantal triangle be represented by T , the surface of the sphere will be repre- sented by 8T . Now , if the right angle be assumed as unity , and the angle of the ...
Page 235
... quadrantal triangle . Let A B C be a spherical triangle ; its area is equal to the excess of the sum of its angles , A , B , C , above two right angles multiplied by the quadrantal triangle . For produce the sides of the triangle A B C ...
... quadrantal triangle . Let A B C be a spherical triangle ; its area is equal to the excess of the sum of its angles , A , B , C , above two right angles multiplied by the quadrantal triangle . For produce the sides of the triangle A B C ...
Page 236
... quadrantal triangle . 564. Cor . If the sum of the three angles of a spherical triangle is equal to three right angles , its area is equal to the quadrantal triangle , or to an eighth part of the surface of the sphere ; if the sum is ...
... quadrantal triangle . 564. Cor . If the sum of the three angles of a spherical triangle is equal to three right angles , its area is equal to the quadrantal triangle , or to an eighth part of the surface of the sphere ; if the sum is ...
Page 237
... quadrantal triangle . 566. Cor . If the sum of all the angles of a spherical polygon be denoted by S , the number of sides by n , the quadrantal triangle by T , and the right angle be regarded as unity , the area of the polygon will be ...
... quadrantal triangle . 566. Cor . If the sum of all the angles of a spherical polygon be denoted by S , the number of sides by n , the quadrantal triangle by T , and the right angle be regarded as unity , the area of the polygon will be ...
Other editions - View all
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 77 - Two rectangles having equal altitudes are to each other as their bases.
Page 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.
Page 313 - FRACTION is a negative number, and is one more tftan the number of ciphers between the decimal point and the first significant figure.
Page 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.
Page 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'.
Page 244 - RULE. — Multiply the base by the altitude, and the product will be the area.