Elements of Geometry: With Practical Applications to Mensuration |
From inside the book
Results 1-5 of 85
Page 43
... example , with the remainder DF . From the first remainder BE , cut off a part equal to the second D F , as many times as possible ; once , for ex- ample , with the remainder B G. From the second re- mainder DF , cut off a BOOK II RATIO ...
... example , with the remainder DF . From the first remainder BE , cut off a part equal to the second D F , as many times as possible ; once , for ex- ample , with the remainder B G. From the second re- mainder DF , cut off a BOOK II RATIO ...
Page 69
... example , that the angles ACB , DCE , at the center of equal circles , are to each other as 7 to 4 ; or , which amounts to the same thing , that the angle M , which will serve as a common measure , is con- A Ρ q M B E tained seven times ...
... example , that the angles ACB , DCE , at the center of equal circles , are to each other as 7 to 4 ; or , which amounts to the same thing , that the angle M , which will serve as a common measure , is con- A Ρ q M B E tained seven times ...
Page 79
... example , as the numbers 7 and 4. If A B is divided into seven equal parts , A E will contain four of those parts . At each point of division draw lines perpendicular to the base ; seven rectangles will thus be formed , all equal to ...
... example , as the numbers 7 and 4. If A B is divided into seven equal parts , A E will contain four of those parts . At each point of division draw lines perpendicular to the base ; seven rectangles will thus be formed , all equal to ...
Page 131
... example , six . Through the extremity A draw the indefinite straight A D E line A E , making any angle with AB . Take AC of any convenient length , and apply it six times upon A E. Join the last point of division , E , and the extremity ...
... example , six . Through the extremity A draw the indefinite straight A D E line A E , making any angle with AB . Take AC of any convenient length , and apply it six times upon A E. Join the last point of division , E , and the extremity ...
Page 195
... example , as 15 is to 8. Divide A E into 15 equal parts , of which AI will contain 8. Through x , y , z , & c . , the points of division , conceive planes to oi E H G 0 F M L z y I D B C E H G 0 F M L K 140 I BOOK VIII . 195.
... example , as 15 is to 8. Divide A E into 15 equal parts , of which AI will contain 8. Through x , y , z , & c . , the points of division , conceive planes to oi E H G 0 F M L z y I D B C E H G 0 F M L K 140 I BOOK VIII . 195.
Other editions - View all
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.