Elements of Geometry: With Practical Applications to Mensuration |
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Page 8
... taken , the straight line that joins them will lie wholly in the surface . 11. A CURVED SURFACE is one that is not a plane sur- face , nor made up of plane surfaces . 12. A SOLID , or VOLUME , is that which has length , breadth , and ...
... taken , the straight line that joins them will lie wholly in the surface . 11. A CURVED SURFACE is one that is not a plane sur- face , nor made up of plane surfaces . 12. A SOLID , or VOLUME , is that which has length , breadth , and ...
Page 13
... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the sums will be unequal . 5. If equals be taken from unequals , the remainders will be unequal . 6. Things which are double of the same thing , or ...
... taken from equals , the remainders will be equal . 4. If equals be added to unequals , the sums will be unequal . 5. If equals be taken from unequals , the remainders will be unequal . 6. Things which are double of the same thing , or ...
Page 15
... taken together , to two right angles ; for their sum is equal to that of the two adjacent angles , BAC , CAF . B D C E PROPOSITION II.THEOREM . F A 47. If one straight line meets two other straight lines at a common point , making ...
... taken together , to two right angles ; for their sum is equal to that of the two adjacent angles , BAC , CAF . B D C E PROPOSITION II.THEOREM . F A 47. If one straight line meets two other straight lines at a common point , making ...
Page 26
... taken at pleasure , in the perpendicular , and join DA , DB , and also AE , EB . A4 Then , since AC is equal to CB , the D F E C B two oblique lines D A , D B meet points which are at the same distance from the perpendicular , and are ...
... taken at pleasure , in the perpendicular , and join DA , DB , and also AE , EB . A4 Then , since AC is equal to CB , the D F E C B two oblique lines D A , D B meet points which are at the same distance from the perpendicular , and are ...
Page 44
... taken for unity , the line AB would be ; if AB were taken for unity , CD would be . It is possible that , however far the operation be con- tinued , no remainder may be found which shall be con- tained an exact number of times in the ...
... taken for unity , the line AB would be ; if AB were taken for unity , CD would be . It is possible that , however far the operation be con- tinued , no remainder may be found which shall be con- tained an exact number of times in the ...
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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.