The First Six Books of the Elements of Euclid: With NotesPrinted at the University Press, for R. Milliken and son, 1833 - 183 sider |
Inni boken
Resultat 1-5 av 24
Side 5
... fall on BC ; and because the side DF is equal to BC , the point F must coincide with C. But as the points E and F coincide with the points A and C , the right lines EF and AC must coincide ( 1 ) , ( 1 ) Ax . 10 . and therefore the bases ...
... fall on BC ; and because the side DF is equal to BC , the point F must coincide with C. But as the points E and F coincide with the points A and C , the right lines EF and AC must coincide ( 1 ) , ( 1 ) Ax . 10 . and therefore the bases ...
Side 12
... fall at the side of the obtuse angle , and therefore must fall at the side of the acute angle . Fig . 33 . ( 1 ) Ax . 11 . ( 2 ) Prop.16 . Fig . 31 . Cor . 2. Two perpendiculars cannot be drawn from the same point B , to the same right ...
... fall at the side of the obtuse angle , and therefore must fall at the side of the acute angle . Fig . 33 . ( 1 ) Ax . 11 . ( 2 ) Prop.16 . Fig . 31 . Cor . 2. Two perpendiculars cannot be drawn from the same point B , to the same right ...
Side 16
... fall below the base ( 3 ) , join BG , GC . Since the right lines AG and AC are equal ( 4 ) , the angles ACG and AGC are equal ( 5 ) ; but the angle BGC is greater than AGC , therefore greater than ACG , and therefore greater than BCG ...
... fall below the base ( 3 ) , join BG , GC . Since the right lines AG and AC are equal ( 4 ) , the angles ACG and AGC are equal ( 5 ) ; but the angle BGC is greater than AGC , therefore greater than ACG , and therefore greater than BCG ...
Side 32
... falls . For the square of the side AB is equal to the squares ( 1 ) Prop . 47. of AD and DB ( 1 ) , and the square of BC is equal to the squares of BD and DC ( 1 ) ; therefore the difference between the squares of AB and BC is equal to ...
... falls . For the square of the side AB is equal to the squares ( 1 ) Prop . 47. of AD and DB ( 1 ) , and the square of BC is equal to the squares of BD and DC ( 1 ) ; therefore the difference between the squares of AB and BC is equal to ...
Side 40
... falls ( 1 ) ; and therefore , when the perpendicular falls within the triangle , to the rec- tangle under BC the sum ... fall without the triangle , the difference of the squares of the segments BF and FC is equal to the rectangle under ...
... falls ( 1 ) ; and therefore , when the perpendicular falls within the triangle , to the rec- tangle under BC the sum ... fall without the triangle , the difference of the squares of the segments BF and FC is equal to the rectangle under ...
Vanlige uttrykk og setninger
absurd AC and BD AC and CB AC is equal angle ABC angle ACD angle BAC angle equal base bisected centre circumference Constr constructed contained in CD demonstrated described double the rectangle double the square drawn equal angles equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident external angle fore form one right four magnitudes proportional four right angles fourth given angle given circle given line given right line given triangle gles half a right Hypoth inscribed less line CD manner multiple oftener opposite parallel parallelogram perpendicular PROB produced Prop proposition radius rectangle under AC right angles right line AB Schol segment side AC sides AB similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Populære avsnitt
Side 147 - 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 3 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
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 16 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Side 148 - 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 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 92 - F) a ratio compounded of the ratios which the first has to the second, the second to the third, the third to the fourth (A to D, D to C, and C to F) ; and so on to the last.
Side 93 - AXIOMS. 1. Equimultiples of the same, or of equal magnitudes, are equal to one another. 2. Those magnitudes, of which the same or equal magnitudes are equimultiples, are equal to one another. 3. A multiple of a greater magnitude is greater than the same multiple of a less. 4. That magnitude, of which a multiple is greater than the same multiple of another, is greater than that other magnitude.
Side 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
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.