## An introduction to geometry, consisting of Euclid's Elements, book i, accompanied by numerous explanations, questions, and exercises, by J. Walmsley. [With] Answers, Volume 11884 |

### From inside the book

Page 138

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**of the other , each to each , and have likewise their bases equal**, show that the angle contained by the two sides of the one triangle is equal to that con- tained by the two sides of the other . ( 16 ) * 8. If a quadrilateral figure is ...### Other editions - View all

An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2013 |

An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2023 |

An Introduction to Geometry, Consisting of Euclid's Elements, Book I ... Euclides No preview available - 2018 |

### Common terms and phrases

AB is equal AC is equal adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle BCD angle equal angles CBA axiom base BC bisects the angle centre circle circumference Constr construction Corollary deduce definition diagonal Diagram drawn enunciation equal and parallel equal angles equal sides equal to BC equiangular EQUIANGULAR POLYGONS equilateral triangle Euclid Euclid's Elements exterior four right angles Geometry given point given rectilineal given straight line hypotenuse hypothesis inference isosceles triangle join less Let ABC magnitude meet opposite interior angle opposite sides pair of equal parallel to BC parallelogram perpendicular Playfair's Axiom Postulate produced proof Prop proposition prove quadrilateral rectilineal figure respectively equal rhombus right-angled triangle side BC sides equal square supplementary angles theorems thesis trapezium triangle ABC unequal vertex Wherefore XXVIII

### Popular passages

Page 132 - 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 86 - 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 139 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 133 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Page 134 - Prove that parallelograms on the same base and between the same parallels are equal in area.

Page 134 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.

Page 50 - if two straight lines" &c. QED COR. 1. From this it is manifest, that if two straight lines cut one another, the angles which they make at the point where they cut, are together equal to four right angles.

Page 20 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.

Page 96 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Page 49 - If at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line.