## The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |

### From inside the book

Results 1-5 of 34

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**angle ACB**to the angle DFE . B C E For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE , the point B shall coincide with the point E , because AB is equal to DE ... Page 9

... angle DEF , and the

... angle DEF , and the

**angle ACB**to the angle DFE . Wherefore , If two triangles & c . Q.E. D. PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the ... Page 10

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**angle**ACF to the**angle**ABG and the**angle**AFC to the**angle**AGB : And because the whole AF is equal to the whole AG ...**ACB**( Ax . 3 ) , which are the**angles**at the base of the triangle ABC : And it has been proved that the**angle**FBC ... Page 11

... ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the

... ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the

**angle ACB**( Hyp . ) — therefore the base DC is equal to the base AB ( 1. 4 ) ... Page 12

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**angle**BCD : Again , because BC is equal to BD the**angle**BCD is equal to the**angle**BDC : but it has been proved to be greater than it - which is impossible . F R But , if one of the vertices , as D , be within the other triangle**ACB**...### Other editions - View all

The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides No preview available - 2016 |

### Common terms and phrases

ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore

### Popular passages

Page 42 - 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 4 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 33 - F, which is the common vertex of the triangles: that is », together with four right angles. Therefore all the angles of the figure, together with four right angles are equal to twice as many right angles as the figure has sides.

Page 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 22 - If from the ends of a 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 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.

Page 194 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 2 - 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 : 16.

Page 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.