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Page xi
... whence A : C :: B : D , A : C :: E : F ; B : D :: E : F , • B : E :: D : F. or IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the equality of the product of the extremes to ...
... whence A : C :: B : D , A : C :: E : F ; B : D :: E : F , • B : E :: D : F. or IV . Other changes , besides the transposition of terms , may be made among proportionals without destroying the equality of the product of the extremes to ...
Page xiii
... Whence it follows , that the sum of the antecedents is to their difference as the sum of the consequents is to their difference . If we have a series of equal ratios A : B :: CD :: E : F , by considering only the two first , which form ...
... Whence it follows , that the sum of the antecedents is to their difference as the sum of the consequents is to their difference . If we have a series of equal ratios A : B :: CD :: E : F , by considering only the two first , which form ...
Page xiv
... whence it follows , that the squares of four proportional quantities form a new proportion . by By multiplying the proportion we shall have A2 : B2 : C2 : De Ꭿ : B :: C : Ꭰ , A3 : B3 :: C3 : D3 ; that is , the cubes of four ...
... whence it follows , that the squares of four proportional quantities form a new proportion . by By multiplying the proportion we shall have A2 : B2 : C2 : De Ꭿ : B :: C : Ꭰ , A3 : B3 :: C3 : D3 ; that is , the cubes of four ...
Page 5
... whence straight lines , which have two points common A and B , cannot separate the one from the other , when produced ; therefore they must form one and the same straight line . THEOREM . Fig . 2 33. If two adjacent angles Of ...
... whence straight lines , which have two points common A and B , cannot separate the one from the other , when produced ; therefore they must form one and the same straight line . THEOREM . Fig . 2 33. If two adjacent angles Of ...
Page 7
... be somewhere in CA ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of Perpendicular and Oblique Lines . 7.
... be somewhere in CA ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of Perpendicular and Oblique Lines . 7.
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence