The First Six Books with NotesR. Milliken, 1822 - 179 sider |
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Side 3
... opposite sides are parallel . 31. A square is a quadrilateral figure , which has all its sides equal , and all its angles right angles . 32. Rectilineal figures , which have more than four sides , are called polygons . Postulates . 1 ...
... opposite sides are parallel . 31. A square is a quadrilateral figure , which has all its sides equal , and all its angles right angles . 32. Rectilineal figures , which have more than four sides , are called polygons . Postulates . 1 ...
Side 5
... angles contained by those sides also equal to one another ( D to B ) ; their bases ( EF and AC ) are equal , and the angles at the bases , which are opposite to the equal sides , are equal ( E to A and F to C ) ; and also the triangles ...
... angles contained by those sides also equal to one another ( D to B ) ; their bases ( EF and AC ) are equal , and the angles at the bases , which are opposite to the equal sides , are equal ( E to A and F to C ) ; and also the triangles ...
Side 6
... angles A and C , the angles themselves must coincide , and are therefore equal ( 3 ) . And if the right lines which ... opposite to equal sides . PROP . VI . THEOR . If two angles ( 6 Elements of Euclid .
... angles A and C , the angles themselves must coincide , and are therefore equal ( 3 ) . And if the right lines which ... opposite to equal sides . PROP . VI . THEOR . If two angles ( 6 Elements of Euclid .
Side 7
... opposite to them , ( AC and AB ) are also equal . For if the sides be not ... angles DBC and ACB are also equal ( 2 ) ; therefore the tri- angles ... angle BDC is greater than ADC ( 3 ) , and therefore BDC is greater than BCD but in the ...
... opposite to them , ( AC and AB ) are also equal . For if the sides be not ... angles DBC and ACB are also equal ( 2 ) ; therefore the tri- angles ... angle BDC is greater than ADC ( 3 ) , and therefore BDC is greater than BCD but in the ...
Side 8
... angles ECD and FDC are equal ( 7 ) ; but the angle BDC is greater than FDC ... angles BDC and BCD are equal ( 7 ) ; but the angle BDC has been proved to be greater ... opposite to the equal sides , are equal , and also that the triangles ...
... angles ECD and FDC are equal ( 7 ) ; but the angle BDC is greater than FDC ... angles BDC and BCD are equal ( 7 ) ; but the angle BDC has been proved to be greater ... opposite to the equal sides , are equal , and also that the triangles ...
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Vanlige uttrykk og setninger
absurd AC and BD AC and CB AC are equal alternate angles angle ABC angle ACD angle BAC angle equal base bisected centre circumference CKMB Constr constructed contained in CD demonstrated double the rectangle double the square equal angles equal sides equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident fore four magnitudes proportional four right angles given angle given circle given line given right line given triangle half a right Hypoth inscribed less line CD manner mean proportional multiple oftener parallel parallelogram perpendicular point of contact PROB produced Prop proposition radius rectangle under AC right line AB Schol segment side AC similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Populære avsnitt
Side 145 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 2 - 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.
Side 28 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 22 - 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.
Side 118 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Side 146 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Side 168 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 3 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Side 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.