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 TrigonometryBell & Bradfute, 1804 - 440 páginas |
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Página 22
... THEO R. NY two fides of a triangle are together greater than the third fide . greater Let ABC be a triangle ; any two fides of it together are greater than the third fide , viz . the fides BA , AC than the fide BC ; and AB , BC greater ...
... THEO R. NY two fides of a triangle are together greater than the third fide . greater Let ABC be a triangle ; any two fides of it together are greater than the third fide , viz . the fides BA , AC than the fide BC ; and AB , BC greater ...
Página 39
... it B can be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal tri- angles upon , & c . Q. E. D. D 4 PROP . Book I. 2.31 . T. PROP . XL . THEO OF GEOMETRY . 39.
... it B can be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore equal tri- angles upon , & c . Q. E. D. D 4 PROP . Book I. 2.31 . T. PROP . XL . THEO OF GEOMETRY . 39.
Página 40
... THEO R. QUAL triangles upon equal bafes , in the fame ftraight line , and towards the fame parts , are between the fame parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in the fame ftraight line BF , and to ...
... THEO R. QUAL triangles upon equal bafes , in the fame ftraight line , and towards the fame parts , are between the fame parallels . Let the equal triangles ABC , DEF be upon equal bases BC , EF , in the fame ftraight line BF , and to ...
Página 198
... THEO R. IF F two points be taken in the diameter of a circle , fuch that the rectangle contained by the feg- ments intercepted between them and the centre of the circle be equal to the fquare of the radius ; and if from these points two ...
... THEO R. IF F two points be taken in the diameter of a circle , fuch that the rectangle contained by the feg- ments intercepted between them and the centre of the circle be equal to the fquare of the radius ; and if from these points two ...
Página 375
... theo- rems contained in the above enunciation will give the value of the thing required . Suppofe , for example , that AB and BC are given , to find C ; it is evident that if AB be made the middle part , BC and C are the oppofite parts ...
... theo- rems contained in the above enunciation will give the value of the thing required . Suppofe , for example , that AB and BC are given , to find C ; it is evident that if AB be made the middle part , BC and C are the oppofite parts ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Sin vista previa disponible - 2016 |
Términos y frases comunes
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifected Book cafe centre circle ABC circumference co-fine cof BC cylinder defcribed demonftrated diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame manner fame plane fame ratio fame reaſon fecond fection fegment femicircle fhall fhewn fide BC fides fince firft firſt folid fore fquare fuch given ftraight line greater infcribed interfect join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals Q. E. D. PROP radius reafon rectangle contained rectilineal figure remaining angle ſpherical triangle ſquare tangent THEOR theſe thofe thoſe triangle ABC uſe wherefore
Pasajes populares
Página 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...
Página 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.
Página 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Página 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...
Página 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.
Página 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...
Página 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...
Página 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.
Página 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...
Página 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.