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 |
Inni boken
Resultat 1-5 av 10
Side 21
1 Let ABC be any triangle ; Book I. A any two of its angles together are less than
two right angles . Produce BC to D ; and because ACD is the exterior angle of the
triangle ABC , a 16. I. ACD is greater a than the interior and opposite angle ABC ...
1 Let ABC be any triangle ; Book I. A any two of its angles together are less than
two right angles . Produce BC to D ; and because ACD is the exterior angle of the
triangle ABC , a 16. I. ACD is greater a than the interior and opposite angle ABC ...
Side 71
... DC at right angles to AB , and produce it to E , and bisect CE in F : The point F
is the centre d u . i . of the circle ABC . ... and the base GA is equal to the base GB
, because they are radii of the same circle : therefore the angle ADG is equal c c ...
... DC at right angles to AB , and produce it to E , and bisect CE in F : The point F
is the centre d u . i . of the circle ABC . ... and the base GA is equal to the base GB
, because they are radii of the same circle : therefore the angle ADG is equal c c ...
Side 98
N a circle , the angle in a semicircle is a right angle ; but the angle in a segment
greater than a femicircle is less than a right ... 1. also equal to the two angles ABC
, ACB ; therefore the an B В E C gle BAC is equal to the angle FAC , and each of
...
N a circle , the angle in a semicircle is a right angle ; but the angle in a segment
greater than a femicircle is less than a right ... 1. also equal to the two angles ABC
, ACB ; therefore the an B В E C gle BAC is equal to the angle FAC , and each of
...
Side 111
Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe
in the circle ABC a triangle ... 3 • qual to the angle ABC in the alternate segment
of the circle : But HAC is e . qual to the angle DEF ; therefore also the angle ABC
...
Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe
in the circle ABC a triangle ... 3 • qual to the angle ABC in the alternate segment
of the circle : But HAC is e . qual to the angle DEF ; therefore also the angle ABC
...
Side 162
1. two right angles b , ABC and DEC , which is equal to ACB , are also less than
two right angles : wherefore BA , ED ... 1. meet < ; let them be produced and meet
in the point F ; and because the angle ABC is equal to the angle A d 28. 1.
1. two right angles b , ABC and DEC , which is equal to ACB , are also less than
two right angles : wherefore BA , ED ... 1. meet < ; let them be produced and meet
in the point F ; and because the angle ABC is equal to the angle A d 28. 1.
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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 |