The First Six Books with NotesR. Milliken, 1822 - 179 σελίδες |
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Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 7
... ) , therefore the angles BDC and BCD are equal ( 5 ) but the angle BDC has been 18 proved to be greater than BCD , which is absurd . Therefore the triangles constructed upon the same לי A B L E 116 I 19 c 20 Fig . 19 . ( Book the First . 7.
... ) , therefore the angles BDC and BCD are equal ( 5 ) but the angle BDC has been 18 proved to be greater than BCD , which is absurd . Therefore the triangles constructed upon the same לי A B L E 116 I 19 c 20 Fig . 19 . ( Book the First . 7.
Σελίδα 8
... proved to be greater than BCD , which is absurd . Therefore trian- gles constructed upon the same right line cannot have their conterminous sides equal , if the vertex of one of them is within the other . Thirdly . Let the vertex D of ...
... proved to be greater than BCD , which is absurd . Therefore trian- gles constructed upon the same right line cannot have their conterminous sides equal , if the vertex of one of them is within the other . Thirdly . Let the vertex D of ...
Σελίδα 11
... proved that no other line , ex- cept BD , is the continuation of it ; therefore BD forms with BC one continued right line . PROP . XV . THEOR . If two right lines ( AB and CD ) intersect one ano- ther , the vertical angles are equal ...
... proved that no other line , ex- cept BD , is the continuation of it ; therefore BD forms with BC one continued right line . PROP . XV . THEOR . If two right lines ( AB and CD ) intersect one ano- ther , the vertical angles are equal ...
Σελίδα 46
... proved that CEB is half a right angle , therefore AEB is a right angle , and be- cause DG and EC are parallel ( 5 ) , the alternate angles GDB , ECB are equal , therefore GDB is a right angle ; ( 7 ) Prop.15 also the angles DBG and EBC ...
... proved that CEB is half a right angle , therefore AEB is a right angle , and be- cause DG and EC are parallel ( 5 ) , the alternate angles GDB , ECB are equal , therefore GDB is a right angle ; ( 7 ) Prop.15 also the angles DBG and EBC ...
Σελίδα 53
... proved that no other B. 1 . point without the line CE is the centre ; therefore the ( 7 ) Cons . centre is in the line CE , and therefore is the point F. ( 8 ) Ar . 11 . Schol . Hence it is evident that if any line termi- nated in a ...
... proved that no other B. 1 . point without the line CE is the centre ; therefore the ( 7 ) Cons . centre is in the line CE , and therefore is the point F. ( 8 ) Ar . 11 . Schol . Hence it is evident that if any line termi- nated in a ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.