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 4
Multilateral figures , or polygons , by more than four straight lines . XIX . Of three fided figures , an equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal .
Multilateral figures , or polygons , by more than four straight lines . XIX . Of three fided figures , an equilateral triangle is that which has three equal sides . XX . An isosceles triangle is that which has only two sides equal .
Seite 178
IMILAR polygons may be divided into the same number of fimilar triangles , having the fame ratio to one another ... whereof each has to each the same ratio which the polygons have ; and the polygon ABCDE has to the polygon FGHKL the ...
IMILAR polygons may be divided into the same number of fimilar triangles , having the fame ratio to one another ... whereof each has to each the same ratio which the polygons have ; and the polygon ABCDE has to the polygon FGHKL the ...
Seite 179
56.6 . fore the angle ABE is equal to the angle FGL : and , be- € 4.6 . cause the polygons are similar ... EBC , ECD , and the confequents FGL , LGH , LAK : and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that ...
56.6 . fore the angle ABE is equal to the angle FGL : and , be- € 4.6 . cause the polygons are similar ... EBC , ECD , and the confequents FGL , LGH , LAK : and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that ...
Seite 180
Wherefore , as the triangle ABE to the triangle FGL , so is the polygon ABCDE to the polygon FGHKL but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the fide AB has to the homologous fide FG .
Wherefore , as the triangle ABE to the triangle FGL , so is the polygon ABCDE to the polygon FGHKL but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the fide AB has to the homologous fide FG .
Seite 208
Hence , the perimeter of any polygon inscribed in a circle is less than the circumference of the circle . Cor . 2. If from a point ' two straight lines be drawn touching a circle , these two lines are together greater than the arch ...
Hence , the perimeter of any polygon inscribed in a circle is less than the circumference of the circle . Cor . 2. If from a point ' two straight lines be drawn touching a circle , these two lines are together greater than the arch ...
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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
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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 |