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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Resultat 1-5 av 9
Side 162
Therefore , because it has been proved that AB : BC :: DC : CE ; and BC : CA ::
CE : ED , ex æquali , BA : AC :: CD : DE . Therefore the fides , & c . Q. E. D. .
PROP . V. THEOR . F the sides of two triangles , about each of their angles , be ...
Therefore , because it has been proved that AB : BC :: DC : CE ; and BC : CA ::
CE : ED , ex æquali , BA : AC :: CD : DE . Therefore the fides , & c . Q. E. D. .
PROP . V. THEOR . F the sides of two triangles , about each of their angles , be ...
Side 166
But it was proved that the $ 13. 1 . angle AGB is equal to the angle at F ; therefore
the angle at F is greater than a right angle : But , by the hypothesis , it is less than
a right angle ; which is absurd . Therefore the angles ABC , DEF are not ...
But it was proved that the $ 13. 1 . angle AGB is equal to the angle at F ; therefore
the angle at F is greater than a right angle : But , by the hypothesis , it is less than
a right angle ; which is absurd . Therefore the angles ABC , DEF are not ...
Side 180
Therefore also the polygon ABCDE has to the poly . gon FGHKL the duplicate
ratio of that which AB has to the homologous fide FG . . Wherefore fimilar
polygons , & c . Q. E. D. Cor . 1. In like manner it may be proved , that fimilar four
fided ...
Therefore also the polygon ABCDE has to the poly . gon FGHKL the duplicate
ratio of that which AB has to the homologous fide FG . . Wherefore fimilar
polygons , & c . Q. E. D. Cor . 1. In like manner it may be proved , that fimilar four
fided ...
Side 193
D L G H N K B E M С F the arch EN , and the angle EHN : And it has been proved
, that , if the arch BL be greater than EN , the angle BGL is greater than EHN ; and
if equal , equal ; and if lefs , less : As therefore , the arch BC to the arch EF , so ...
D L G H N K B E M С F the arch EN , and the angle EHN : And it has been proved
, that , if the arch BL be greater than EN , the angle BGL is greater than EHN ; and
if equal , equal ; and if lefs , less : As therefore , the arch BC to the arch EF , so ...
Side 194
For the same reason , the sector KGL is equal to each of the sectors BGC , CGK ;
and in the same manner , the sectors EHF , FHM , MHN may be proved equa ! to
one another : Therefore , what multiple soever the arch BL is of the arch BC , the
...
For the same reason , the sector KGL is equal to each of the sectors BGC , CGK ;
and in the same manner , the sectors EHF , FHM , MHN may be proved equa ! to
one another : Therefore , what multiple soever the arch BL is of the arch BC , the
...
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Vanlige uttrykk og setninger
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 rectangle contained remaining right angles ſame ſame ratio ſecond ſegment ſhall ſides ſimilar ſin ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe third thoſe touches triangle triangle ABC wherefore whole
Populære avsnitt
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.
Bibliografisk informasjon
| Tittel | 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 Volum 109 av Jahn library |
| Forfattere | Euclid, John Playfair |
| Utgave | 2 |
| Utgiver | Bell & Bradfute, 1804 |
| Original fra | Harvard University |
| Digitalisert | 27. apr 2007 |
| Lengde | 440 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |