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

### From inside the book

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**angle**. DEF . 13. An obtuse**angle**is that which is greater than one right**angle**, but less than two right**angles**...**ABC**be a right**angle**formed by the straight line AB standing on the straight line CBD , EFG a right**angle**formed by the ... Page 19

... angle EFH or the angle EFG . Let it fall within the angle EFH , as FK . Then , because the angle KFG is a right ... ABC coincides with the angle EFG , and therefore the

... angle EFH or the angle EFG . Let it fall within the angle EFH , as FK . Then , because the angle KFG is a right ... 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 ... Page 20

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**angle ABC**is equal to the angle ABD , each of them is a right angle , and therefore they are together equal to two right angles . But if the**angle ABC**is not equal to the angle ABD , Def . 10 . let BE be a straight line standing upon ... Page 20

... ABC , ABD is the angle contained by BC , BD , Def . 8 . and this angle is a straight angle , since CBD is a straight line , Def . 7 . therefore the

... ABC , ABD is the angle contained by BC , BD , Def . 8 . and this angle is a straight angle , since CBD is a straight line , Def . 7 . therefore the

**angles ABC**, ABD are together equal to a straight angle , that is , to two right angles ... Page 20

... angle . THEOR . 3. If the adjacent angles made by one straight line with two others are together equal to two right angles , these two straight lines are in one straight line . Let the adjacent ...

... angle . THEOR . 3. If the adjacent angles made by one straight line with two others are together equal to two right angles , these two straight lines are in one straight line . Let the adjacent ...

**angles ABC**, ABD ANGLES AT A POINT . 20C.### 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.