Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 Seiten |
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Seite 17
... coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersec- " tions of one superficies with another are also ...
... coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersec- " tions of one superficies with another are also ...
Seite 21
... coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI ... " Two straight lines which intersect ...
... coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. All right angles are equal to one another . XI ... " Two straight lines which intersect ...
Seite 24
... coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is ...
... coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is ...
Seite 27
... coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but have a different situation as EG and FG ...
... coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC shall coincide with ED , and DF ; for , if BA , and CA do not coincide with ED , and FD , but have a different situation as EG and FG ...
Seite 40
... coinciding with one an- other , which is impossible C ( 11. Ax . ) . The angles AGH , GHD therefore are not un- equal , that is , they are equal to one another . Now , the K D H F angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved ...
... coinciding with one an- other , which is impossible C ( 11. Ax . ) . The angles AGH , GHD therefore are not un- equal , that is , they are equal to one another . Now , the K D H F angle EGB is equal to AGH ( 15. 1. ) ; and AGH is proved ...
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Häufige Begriffe und Wortgruppen
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw drawn 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 parallelepipeds 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 straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Beliebte Passagen
Seite 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Seite 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.
Seite 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Seite 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 308 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 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.
Seite 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.
Seite 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Seite 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.