The First Six Books with NotesR. Milliken, 1822 - 179 σελίδες |
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Αποτελέσματα 1 - 5 από τα 25.
Σελίδα 90
... multiple of a less , when the ... 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 second oftener than an equi ...
... multiple of a less , when the ... 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 second oftener than an equi ...
Σελίδα 92
... Equi - multiples of the same or of equal magnitudes are equal : 2. Those magnitudes of which the same or equal magnitudes are equi - multiples or equi - submultiples , are equal , 3. A multiple or submultiple of a greater magnitude is ...
... Equi - multiples of the same or of equal magnitudes are equal : 2. Those magnitudes of which the same or equal magnitudes are equi - multiples or equi - submultiples , are equal , 3. A multiple or submultiple of a greater magnitude is ...
Σελίδα 93
... equi - multiples of B. 1 . the same A , and therefore BC is equal to Dm ( 1 ) , but BC is equal to DE ( 2 ) , therefore Dm is equal to DE ( 3 ) , which is absurd . Now , if it be possible , let A be oftener contained in BC than in DE ...
... equi - multiples of B. 1 . the same A , and therefore BC is equal to Dm ( 1 ) , but BC is equal to DE ( 2 ) , therefore Dm is equal to DE ( 3 ) , which is absurd . Now , if it be possible , let A be oftener contained in BC than in DE ...
Σελίδα 94
... multiple of A , the other is also an equi - multiple of A. Cor . 2. If two magnitudes be equal , as often as one of them is contained in any third , so other contained in the same third . often is the first equal Cor . 3. If there be ...
... multiple of A , the other is also an equi - multiple of A. Cor . 2. If two magnitudes be equal , as often as one of them is contained in any third , so other contained in the same third . often is the first equal Cor . 3. If there be ...
Σελίδα 95
... equi - multiples of A and B ( 1 ) , and A is ( 1 ) Cnstr . greater than B ( 2 ) , Cm is greater than EF ( 3 ) , but EF ( 2 ) Hypoth . is equal to CD ( 2 ) , therefore Cm is greater than CD , B. 5 . which is absurd . ( 5 ) Ax . 3 . 2 ...
... equi - multiples of A and B ( 1 ) , and A is ( 1 ) Cnstr . greater than B ( 2 ) , Cm is greater than EF ( 3 ) , but EF ( 2 ) Hypoth . is equal to CD ( 2 ) , therefore Cm is greater than CD , B. 5 . which is absurd . ( 5 ) Ax . 3 . 2 ...
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.