## Elements of Geometry: Containing the First Six Books of Euclid, with Two Books on the Geometry of Solids. To which are Added, Elements of Plane and Spherical Trigonometry |

### From inside the book

Results 1-5 of 19

Page 20

... exterior Tangle is greater than either of the interior oppo- fite angles . Let ABC be a triangle , and let its fides BC be produced to D , the

... exterior Tangle is greater than either of the interior oppo- fite angles . Let ABC be a triangle , and let its fides BC be produced to D , the

**exterior angle**ACD is greater than either of the interior opposite angles CBA , BAC . Bifecta ... Page 21

... angles toge- ther are less than two right angles . Book I. Produce BC to D ; and because ACD is the

... angles toge- ther are less than two right angles . Book I. Produce BC to D ; and because ACD is the

**exterior angle**of the triangle ABC , ACD is greater a than the interior and oppofite angle ABC ; to each of these add the angle ACB ... Page 23

... angle BCD of the triangle . DCB is greater than its - Book I angle BDC , and that the greater c fide is opposite to ...

... angle BCD of the triangle . DCB is greater than its - Book I angle BDC , and that the greater c fide is opposite to ...

**exterior angle**of a triangle is greater than the interior and opposite angle , the**exterior angle**BDC of the ... Page 29

... angle BCA ; therefore also Book I. the angle BHA is equal to the angle BCA , that is , the exte- rior angle BHA of ...

... angle BCA ; therefore also Book I. the angle BHA is equal to the angle BCA , that is , the exte- rior angle BHA of ...

**exterior angle**AEF is greater than the a 16 . interior and oppofite angle EFG ; but it is also equal to it ... Page 30

...

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**exterior angle**EGB equal to the in- terior and oppofite angle GHD upon the same fide ; or make the interior angles on the fame fide BGH , A GHD together equal to two right angles ; AB is parallel to CD . E G B H D F Because the angle ...### Other editions - View all

### Common terms and phrases

ABCD alfo alſo alſo equal angle ABC angle ACB angle BAC arch baſe baſe BC BC is equal becauſe becauſe the angle biſected Book VII caſe cauſe centre circle ABC circumference co-fine demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fame reaſon fides fimilar fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepiped parallelogram paſs paſſes perpendicular plane polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſame ſame manner ſame ratio ſecond ſection ſegment ſhall be equal ſhewn ſide ſolid ſpace ſpherical triangle ſquare of AC ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC wherefore

### Popular passages

Page 19 - 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. either the sides adjacent to the equal...

Page 155 - 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 17 - 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, these two straight lines shall be in one and the same straight line.

Page 9 - Wherefore, from the given point A, a straight line AL has been drawn equal to the given straight line BC.

Page 3 - 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 23 - 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 12 - ABC: and it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore the angles at the base, &c.

Page 6 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 156 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...

Page 44 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...