## Skeleton propositions &c. of Euclid, books i and ii, with references, by H. Green, Volume 11868 |

### Common terms and phrases

12 Recap 9 Ax 9 Concl 9 Recap adjacent Algebra and Arithmetic alternate angles equal angle contained angle triangle apply BOOKS OF EUCLID Construction and Demonstration consult the Gradations Data describe a parallelogram DIAGRAMS equal and parallel equal angles equal bases equal sides Equal triangles EUCLID BOOKS EXERCISES EXPLANATORY PREFACE Exposition four rt GEOMETRICAL REASONING GEOMETRY given in numbers given point given rectilineal angle given st given triangle GRADATIONS IN EUCLID greater angle hypotenuse Learner Let the equal line falling margin opposite parallel st parallels are equal PEN-AND-INK EXAMINATIONS perp PRICE Principles printed PROB PROP Quæs recapitulatory rectil rectilineal figure references SCHOL SECOND BOOKS segments Series side equal side together equal SKELETON PROPOSITIONS squares be given squares described step by step THEOR third angle Triangles upon equal truths uniformity vertex vertical written دو وو

### Popular passages

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.

Page xxxviii - Triangles upon equal bases, and between the same parallels, are equal to one another.