## Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements |

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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid No preview available - 2008 |

### Common terms and phrases

AC is equal acute alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid extended exterior angle extremities four right angles geometers geometry given point given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means measurement meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle problem produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AB side AC surfaces THEOR theorem thing third triangle ABC triangles are equal truths unequal vertex wherefore whole

### Popular passages

Page 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.

Page 46 - Any two angles of a triangle are together less than two right angles.

Page 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Page 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.

Page 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.

Page 68 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 34 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.

Page 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.

Page 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.