The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 90
... Ratio is a mutual relation of two magnitudes of the same kind , with respect to quantity . 4. Magnitudes are said to have a ratio to each other , if they be such that the less can be multiplied so as to exceed the greater . 5 ...
... Ratio is a mutual relation of two magnitudes of the same kind , with respect to quantity . 4. Magnitudes are said to have a ratio to each other , if they be such that the less can be multiplied so as to exceed the greater . 5 ...
Page 91
... ratio A to B ) . 12. If there be any number of magnitudes of the same See N. kind ( A , D , C and F ) the first is said to have to the last ( A to F ) a ratio compounded of the ratios which the first has to the second , the second to ...
... ratio A to B ) . 12. If there be any number of magnitudes of the same See N. kind ( A , D , C and F ) the first is said to have to the last ( A to F ) a ratio compounded of the ratios which the first has to the second , the second to ...
Page 92
... ratio , the first is to the last in the first series , as the first to the last in the second series . Of this there are two species . 20. Ex æquo ordinate , when the first magnitude is to the second in the first series as the first to ...
... ratio , the first is to the last in the first series , as the first to the last in the second series . Of this there are two species . 20. Ex æquo ordinate , when the first magnitude is to the second in the first series as the first to ...
Page 102
... ratio to the same magnitude ( C ) . And the same magnitude ( C ) has the same ratio to equal magnitudes ( A and B ) . Part 1. Take any equi - submultiples a and b of the equal magnitudes A and B , these submultiples are equal ( 1 ) ...
... ratio to the same magnitude ( C ) . And the same magnitude ( C ) has the same ratio to equal magnitudes ( A and B ) . Part 1. Take any equi - submultiples a and b of the equal magnitudes A and B , these submultiples are equal ( 1 ) ...
Page 103
... ratio than the greater . And any magnitude ( C ) has to the less ( A ) a greater ratio than to the greater ( B ) . Part 1. Since A is less than B , a submultiple of A can be taken which is contained in C oftener than an equi ...
... ratio than the greater . And any magnitude ( C ) has to the less ( A ) a greater ratio than to the greater ( B ) . Part 1. Since A is less than B , a submultiple of A can be taken which is contained in C oftener than an equi ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.