The First Six Books of the Elements of Euclid: With NotesPrinted at the University Press, for R. Milliken and son, 1833 - 183 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 91
... often as an equi - submultiple of the third is contained in the fourth . 6. Magnitudes which have the same ratio are called proportionals . 7. If a submultiple of the first be contained in the Sec N. second oftener than an equi ...
... often as an equi - submultiple of the third is contained in the fourth . 6. Magnitudes which have the same ratio are called proportionals . 7. If a submultiple of the first be contained in the Sec N. second oftener than an equi ...
Σελίδα 94
... oftener contained in BC than in DE ; take away A as often as it is possible from DE , and a part mE shall remain less than A ; take it away as often from BC , and since it is contained in BC oftener than in DE , a part nC shall remain ...
... oftener contained in BC than in DE ; take away A as often as it is possible from DE , and a part mE shall remain less than A ; take it away as often from BC , and since it is contained in BC oftener than in DE , a part nC shall remain ...
Σελίδα 95
... oftener than in DE ; but it is contained as often ( 2 ) , which is absurd ; therefore neither of the given ( 2 ) ... oftener than the second in the fourth . 1. Let B be a submultiple of EF ; and , if it be pos- sible , let A be contained ...
... oftener than in DE ; but it is contained as often ( 2 ) , which is absurd ; therefore neither of the given ( 2 ) ... oftener than the second in the fourth . 1. Let B be a submultiple of EF ; and , if it be pos- sible , let A be contained ...
Σελίδα 96
... oftener than B is contained in EF ; take away B as often as possible from EF , and there shall remain nF less than B ; take away A as often from CD , and since A is contained in CD oftener than B is contained in EF , the remainder mD is ...
... oftener than B is contained in EF ; take away B as often as possible from EF , and there shall remain nF less than B ; take away A as often from CD , and since A is contained in CD oftener than B is contained in EF , the remainder mD is ...
Σελίδα 97
... oftener than in the other ( CD ) , the latter ( CD ) is less than the former . If e be a submultiple of CD , take it ... oftener than in CD ( 1 ) , the remainder mB is greater than e , or equal to it , and therefore greater than nD ; but ...
... oftener than in the other ( CD ) , the latter ( CD ) is less than the former . If e be a submultiple of CD , take it ... oftener than in CD ( 1 ) , the remainder mB is greater than e , or equal to it , and therefore greater than nD ; but ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
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 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.
Σελίδα 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.
Σελίδα 2 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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.
Σελίδα 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.
Σελίδα 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
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.