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 TrigonometryG. Long, 1819 - 333 sider |
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Resultat 1-5 av 66
Side 23
... shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ...
... shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ...
Side 33
... shewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two ...
... shewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two ...
Side 34
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of ...
Side 37
... shewn that it is not equal to it : therefore AA B E F the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two angles of ...
... shewn that it is not equal to it : therefore AA B E F the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of the one equal to two angles of ...
Side 41
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. PROP . XXXI ...
... shewn that the angle AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. PROP . XXXI ...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Side 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 130 - 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 76 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 18 - 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.
Side 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.