## The Elements of Plane Geometry ...W.S. Sonnenschein and Company, 1884 - Geometry, Modern |

### From inside the book

Results 1-5 of 34

Page 9

... of a line parallel to another under various conditions and

... of a line parallel to another under various conditions and

**hence**the division of lines into - aliquot parts , in given ratio , etc. 6. The construction of a triangle , having given ( SYLLABUS OF GEOMETRICAL CONSTRUCTIONS. Page 13

...

...

**Hence**the four associated Theorems ( i ) ( ii ) ( iii ) ( iv ) resolve themselves into two Theorems that are in- dependent of one another , and two others that are always and necessarily true if the former are true ; consequently it ... Page 16

...

...

**Hence**, a . Any straight line may be made to fall on any other straight line with any given point on the one on any given point on the other ; B. Two straight lines which meet in one point cannot meet again unless they coincide ... Page 17

...

...

**Hence**a straight angle is equal to two right angles ; or , a right angle is half a straight angle . DEF . II . A perpendicular to a straight line is a straight line that makes a right angle with it . C DEF . 12. An acute angle is that ... Page 19

...

...

**Hence**the line BA does fall on the line FE . Therefore the angle ABC coincides with the angle EFG , and therefore the angle ABC is equal to the angle EFG . Ax . 1 . Q.E.D. COR . 1. At a given point in a given straight line only one ...### Other editions - View all

### Common terms and phrases

AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisectors bisects centre circle cutting Constr construct a triangle contrapositive diagonal equal angles equal to AC exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral radius rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC side DF sides equal square on AC squares on AB straight angle straight line drawn Theorem trapezium triangle ABC triangle DEF triangles are identically twice the rectangle vertex

### Popular passages

Page 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 70 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 56 - ... is equal to twice as many right angles as the polygon

Page 101 - Prove that parallelograms on the same base and between the same parallels are equal in area.

Page 35 - Any two sides of a triangle are together greater than the third side.

Page 26 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.

Page 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 85 - The locus of a point at a given distance from a given point is the circumference described from the point with the given distance as radius.

Page 42 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 110 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.