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 TrigonometryBell & Bradfute, 1804 - 440 sider |
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Side 23
... angle BDC greater than the angle BAC . D Produce BD to E ; and because two fides of a triangle a are a 20. 1 . greater than the third fide , the two fides BA , AE of the tri- angle ABE are greater than BE . To each of these add EC ...
... angle BDC greater than the angle BAC . D Produce BD to E ; and because two fides of a triangle a are a 20. 1 . greater than the third fide , the two fides BA , AE of the tri- angle ABE are greater than BE . To each of these add EC ...
Side 24
... angle BDC greater than the angle BAC . Therefore , if from the ends of , & c . Q. E. D , PROP . XXII . PROB . a 20. I. a 3. I. T O conftruct a triangle of which the fides fhall be equal to three given straight lines ; but any two ...
... angle BDC greater than the angle BAC . Therefore , if from the ends of , & c . Q. E. D , PROP . XXII . PROB . a 20. I. a 3. I. T O conftruct a triangle of which the fides fhall be equal to three given straight lines ; but any two ...
Side 26
... angle EDG equal to the angle BAČ : and make DG equal b to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two fides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is e- qual to the angle ...
... angle EDG equal to the angle BAČ : and make DG equal b to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two fides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is e- qual to the angle ...
Side 27
... angle BAC is likewife greater than the angle EDF . a D For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal a to EF ; but it is ...
... angle BAC is likewife greater than the angle EDF . a D For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal a to EF ; but it is ...
Side 28
... angle BAC to the third angle EDF . a 4. 1 . a For , if AB be not equal to DE , one of them must be the greater . Let AB be the greater of the two , and make BG equal to DE , and join GC ; therefore , because BG is equal to DE , and BC ...
... angle BAC to the third angle EDF . a 4. 1 . a For , if AB be not equal to DE , one of them must be the greater . Let AB be the greater of the two , and make BG equal to DE , and join GC ; therefore , because BG is equal to DE , and BC ...
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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
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Side 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...
Side 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.
Side 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Side 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...
Side 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.
Side 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...
Side 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...
Side 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.
Side 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...
Side 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.