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 |
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Page xi
... greater than the circumference of that circle , and the other to be less . In the fame man- ner , the quadrature of the circle is performed only by approximation , or by finding two rect- angles , nearly equal to one another , the one ...
... greater than the circumference of that circle , and the other to be less . In the fame man- ner , the quadrature of the circle is performed only by approximation , or by finding two rect- angles , nearly equal to one another , the one ...
Page xiv
... greater than the third , neither could it be true , that the great- er fide of every triangle is oppofite to the greater angle , nor that the equal fides are opposite to equal angles , nor , lastly , that things equal to the fame thing ...
... greater than the third , neither could it be true , that the great- er fide of every triangle is oppofite to the greater angle , nor that the equal fides are opposite to equal angles , nor , lastly , that things equal to the fame thing ...
Page 9
... greater . It is required to cut off from AB , the greater , а part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the centre A , and at the distance AD , describe b the circle DEF ; and ...
... greater . It is required to cut off from AB , the greater , а part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the centre A , and at the distance AD , describe b the circle DEF ; and ...
Page 12
... greater than the other : Let AB be the greater , and from it cut a off DB e- qual to AC , the less , and join DC ; there- A fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to 4. 1 . both , the two fides DB ...
... greater than the other : Let AB be the greater , and from it cut a off DB e- qual to AC , the less , and join DC ; there- A fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to 4. 1 . both , the two fides DB ...
Page 13
... greater than the angle BCD ; therefore the A B angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal a to the angle BCD ; but it has ...
... greater than the angle BCD ; therefore the A B angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal a to the angle BCD ; but it has ...
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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...