Elements of Geometry;: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |
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Page 2
... angle is the inclination of two straight lines to one another , which meet together , but are not in the fame ... ABC , or CBA ; that which is contained by AB , BD is named the angle ABD , or DBA ; and that which is con- tained by BD ...
... angle is the inclination of two straight lines to one another , which meet together , but are not in the fame ... ABC , or CBA ; that which is contained by AB , BD is named the angle ABD , or DBA ; and that which is con- tained by BD ...
Page 10
... triangle DEF ; and the other angles , to B C E F which the equal fides are oppofite , fhall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle ...
... triangle DEF ; and the other angles , to B C E F which the equal fides are oppofite , fhall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle ...
Page 11
... angle ABC fhall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF , the less , and join FC , GB . a A Becaufe AF is equal to AG , and AB to AC , the ...
... angle ABC fhall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF , the less , and join FC , GB . a A Becaufe AF is equal to AG , and AB to AC , the ...
Page 12
... angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it has alfo been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other fide of ...
... angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it has alfo been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other fide of ...
Page 14
... angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , fo that the point B be on E , and the ftraight line BC up- on EF ; the point C fhall alfo coincide with the point F , because BC is equal ...
... angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , fo that the point B be on E , and the ftraight line BC up- on EF ; the point C fhall alfo coincide with the point F , because BC is equal ...
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Common terms and phrases
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifected Book cafe centre circle ABC circumference co-fine cof BC cylinder defcribed demonftrated diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame manner fame plane fame ratio fame reaſon fecond fection fegment femicircle fhall fhewn fide BC fides fince firft firſt folid fore fquare fuch given ftraight line greater infcribed interfect join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals Q. E. D. PROP radius reafon rectangle contained rectilineal figure remaining angle ſpherical triangle ſquare tangent THEOR theſe thofe thoſe triangle ABC uſe wherefore
Popular passages
Page 27 - 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 172 - 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 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Page 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Page 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...
Page 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Page 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.
Page 54 - 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...
Page 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.