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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Seite 10
AB to DF , and AC D to DF ; and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to B С E which the equal fides are opposite , shall be ...
AB to DF , and AC D to DF ; and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to B С E which the equal fides are opposite , shall be ...
Seite 14
The augle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal ...
The augle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal ...
Seite 15
PROB , TO O bisect a given rectilineal angle , that is , to divide it into two equal angles , Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut a off AE e .
PROB , TO O bisect a given rectilineal angle , that is , to divide it into two equal angles , Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut a off AE e .
Seite 20
I. Let ABC be a triangle , and let its fide BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , А F BAC . Bisect a AC in E , join BE and produce it to F , and make EF equal to BE ...
I. Let ABC be a triangle , and let its fide BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , А F BAC . Bisect a AC in E , join BE and produce it to F , and make EF equal to BE ...
Seite 21
Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , a 16.1 . ... In like manner , it may be demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles ...
Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , a 16.1 . ... In like manner , it may be demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles ...
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ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſected Book called caſe centre circle circle ABC circumference coincide common cylinder definition demonſtrated deſcribed diameter difference divided draw drawn equal equal angles equiangular Euclid extremity fall fame fides firſt folid fore four fourth given given ſtraight line greater half inſcribed join leſs Let ABC magnitudes meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved radius ratio rectangle contained remaining right angles ſame ſame reaſon ſecond ſegment ſhall ſides ſimilar ſin ſince ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe thing third thoſe touches triangle ABC wherefore whole
Beliebte Passagen
Seite 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...
Seite 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.
Seite 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Seite 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...
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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...
Seite 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.
Bibliografische Informationen
| Titel | 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 Band 109 von Jahn library |
| Autor/in | John Playfair |
| Ausgabe | 2 |
| Verlag | Bell & Bradfute, 1804 |
| Original von | Harvard University |
| Digitalisiert | 27. Apr. 2007 |
| Länge | 440 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |