## The First Six Books of the Elements of Euclid, with a Commentary and Geometrical Exercises: To which are Annexed a Treatise on Solid Geometry, and a Short Essay on the Ancient Geometrical Analysis |

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A B and B C A B and C D A B C A B D axiom B C is equal bisect Book centre circumference circumscribed cone conical surface const constructed cylinder demonstration diagonal diameter difference draw equal angles equiangular equilateral triangle equimultiples Euclid external angle extremities geometry given circle given line given point given right line greater Hence homologous sides hypotenuse inscribed intersect isosceles triangle less magnitudes multiple parallel parallelogram parallelopiped pentagon perpendicular polygon prism problem Proposition proved pyramid radii radius rectilinear figure respectively equal right line A B segment sides A B similar solid angle square of A C surface tangent Theorem third tiples triangle B A C vertex

### Popular passages

Page 36 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.

Page 44 - 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 52 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.

Page 148 - ... be equimultiples, the one of the second, and the other of the fourth. Let A the first be the same multiple of B the second, that C the third is of D the fourth ; and of A, C let equimultiples EF, GH be taken.

Page 166 - ... If there be three magnitudes, and other three, which have the same ratio taken two and two, but in a cross order; then if the first magnitude be greater than the third, the fourth shall be greater than the sixth: and if equal, equal; and if less, less.

Page 158 - N ; and if equal, equal ; and if less, less : but if G be greater than L, it has been shown that L HC K E M F N H is greater than M ; and if equal, equal; and if less, less: therefore, if G be greater than L, K is greater than N ; and if equal, equal ; and if less less : and G, K are any equimultiples whatever of A, E ; and L, N any whatever of B, F : therefore as A is to B, so is E to F (5.

Page 320 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.

Page 153 - IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth...

Page 153 - THEOR. IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...

Page 155 - D (as in fig. 2 and 3), this magnitude can be multiplied, so as to become greater than D, whether it be AC, or CB. Let it be multiplied until it...