12 Recap 9 Ax 9 Concl 9 Recap adjacent Algebra and Arithmetic already angle contained angle equal anot apply BOOKS OF EUCLID circle Construction and Demonstration consult the Gradations course Data describe a parallelogram DIAGRAMS difference drawn equal and parallel equal angles equal bases equal sides EXERCISES EXPLANATORY PREFACE GEOMETRICAL REASONING GEOMETRY given st Gradations greater greater angle knowledge Learner Let the equal line falling margin method Natural opposite P'st parallels are equal PEN-AND-INK EXAMINATIONS perp PRICE Principles printed PROB Progress PROP Quæs recommended rectilineal figure references respecting SCHOL SECOND BOOKS segments Series side equal side together equal sides similar simultaneously SKELETON PROPOSITIONS squares be given squares described strict Student THEOR third angle triangle truths uniformity various vertex vertical write written Нур دو
Page xxiv - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Page xx - Therefore any two sides, &c. QED PROP. XXI. THEOR. If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Page xxiv - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal angles, or...
Page xli - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page xliii - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Page xxxviii - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Page xxi - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Page xl - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.