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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volumen2
Vista completa - 1858
9 Concl already angle contained angle equal angle triangle apply BOOKS OF EUCLID circle Construction and Demonstration consult the Gradations Data Definitions describe a parallelogram difference double drawn equal angles equal bases GEOMETRY giren given point given st greater greater angle half knowledge Learner Let the equal line falling margin method mind opposite parallel st parallelogram parallels are equal PEN-AND-INK EXAMINATIONS PRACTICAL PRICE Principles printed PROB produced Progress proofs Prop Quæs Recap recapitulatory exercise rectil rectilineal angle rectilineal figure references REMARKS respecting SCHOL SECOND BOOKS Series side equal sides simultaneously SKELETON PROPOSITIONS squares be given squares described step by step Theor third angle triangle truths uniformity various vertex vertical write written XLIII XLVI XLVII XXII XXIV XXIX XXVI XXXVIII Нур
Página 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.
Página 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.
Página 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...
Página 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.
Página 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...
Página xxxviii - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Página 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.
Página 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.