The Elements of Euclid: With Many Additional Propositions, & Explanatory Notes, Etc, Parte1John Weale, 1853 - 136 páginas |
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Página 11
... angles at the bases , which are opposite to the equal sides , will be equal ( E to B and F to C ) ; [ 3 ] and the triangles themselves will be equal . 13 E DEMONSTRATION . For , if the triangle ABC be applied to DEF , so that the point ...
... angles at the bases , which are opposite to the equal sides , will be equal ( E to B and F to C ) ; [ 3 ] and the triangles themselves will be equal . 13 E DEMONSTRATION . For , if the triangle ABC be applied to DEF , so that the point ...
Página 12
... angles of the one equal to the similar angle of the other , and yet for the triangles them- selves not to be equal . Thus , let ABC be a triangle in which neither A nor C are right angles and A is less than C ; then from B as a center ...
... angles of the one equal to the similar angle of the other , and yet for the triangles them- selves not to be equal . Thus , let ABC be a triangle in which neither A nor C are right angles and A is less than C ; then from B as a center ...
Página 13
... angle A is common to both ; therefore the base CF is equal to the base BG ... ABC , will be equal ( g ) , which are the angles at the base of the given ... ABC be turned over on the plane ( see scholium 3 to the preceding pro- position ) ...
... angle A is common to both ; therefore the base CF is equal to the base BG ... ABC , will be equal ( g ) , which are the angles at the base of the given ... ABC be turned over on the plane ( see scholium 3 to the preceding pro- position ) ...
Página 14
... ABC to the lesser DBC , which is absurd ; therefore neither of the sides AC or AB being greater than the other , they are equal . COROLLARY . Hence every equiangular triangle is also equi- lateral , which may be shown by taking each ...
... ABC to the lesser DBC , which is absurd ; therefore neither of the sides AC or AB being greater than the other , they are equal . COROLLARY . Hence every equiangular triangle is also equi- lateral , which may be shown by taking each ...
Página 15
... angle ECD is greater than the angle BCD ( c ) ; and because FDC and ECD are ... ( ABC and DEF ) have two sides of the one respectively equal to two sides of ... ABC be applied to the triangle DEF , so that their equal bases may coincide ...
... angle ECD is greater than the angle BCD ( c ) ; and because FDC and ECD are ... ( ABC and DEF ) have two sides of the one respectively equal to two sides of ... ABC be applied to the triangle DEF , so that their equal bases may coincide ...
Otras ediciones - Ver todas
The elements of Euclid, [books I.-VI. XI. XII.] with many additional ... Eucleides Vista completa - 1853 |
The Elements of Euclid with Many Additional Propositions and Explanatory Notes Henry Law,Eucleides Sin vista previa disponible - 2016 |
Términos y frases comunes
AC and CB AC is equal angle ABC angle BCD angle equal area to double area to twice bisect chord circle ABC circumference Constr CONSTRUCTION COROLLARY DB is equal DEMONSTRATION diagonal divided double the rectangle draw equal angles equal in area equal to AC equilateral Euclid external angle Find the center finite straight line Geometry given angle given line greater Hypoth HYPOTHESES intersect join less line BC lines be drawn magnitude major premiss opposite sides parallel parallelogram perpendicular predicate premises produced proposition quadratic equation reductio ad absurdum right angles SCHOLIA SCHOLIUM second power segment sides AC square on AC square on half squares on AB syllogism termed THEOREM THEOREM.-If triangle ABC twice the rectangle twice the square vertex whole line
Pasajes populares
Página 24 - 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.
Página 114 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Página xiv - 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 : 16. And this point is called the centre of the circle.
Página 13 - The difference between any two sides of a triangle is less than the third side.
Página 111 - AFC. (in. 21.) Hence in the triangles ADE, AFC, there are two angles in the one respectively equal to two angles in the other, consequently, the third angle CAF is equal to the third angle DAB ; therefore the arc DB is equal to the arc CF, (in.
Página 89 - ... the centre of the circle shall be in that line. Let the straight line DE touch the circle ABC in C, and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA.
Página 70 - EQUAL circles are those of which the diameters are equal, or from the centres of which the straight lines to the circumferences are equal. ' This is not a definition, but a theorem, the truth of ' which is evident; for, if the circles be applied to one ' another, so that their centres coincide, the circles ' must likewise coincide, since the straight lines from
Página 34 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.
Página 22 - 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...