Syllabus of Plane' Geometry: (Corresponding to Euclid, book I-Vi) ; Prepared As An Introduction ...
Syllabus of Plane' Geometry: (Corresponding to Euclid, book I-Vi) ; Prepared As An Introduction ...
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The ratio of one magnitude to another is greater that that of a third magnitude to a fourth, when it is possible to find equi- multiples of the antecedents and equimul- tiples of the consequents, such that while the multiple of the antecedent of the first ratio is greater than, or equal to, that of its con- sequent, the multiple of the antecedent of the second ratio is not greater or is less, than that of its consequent.
Def. 55. Two ratios are said to be reciprocal when the antecedent and the ...consequent of one are the consequent and the antecedent of the other, respectively.
SYLLABUB OF PLANE GEOMETRY. .23 Theor. E. Ratios which are equal to the same ratio are equal to one another.
Prop. 23. If two ratios are equal, their reciprocal ratios are equal.
Prop. 24. Equal magnitudes have the same ratio to the same magnitude; and the same magni- tude has the same ratio to equal magnitudes.
Prop. 25. Of two unequal magnitudes, the greater has a greater ratio to a third magnitude than the less has; and the same magnitude has a greater ratio to the less of two magni- tudes than it has to the greater.
What to read after Syllabus of Plane' Geometry: (Corresponding to Euclid, book I-Vi) ; Prepared As An Introduction ...?
You can find similar books in the "Read Also" column, or choose other free books by Williams Cora Lenore to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The ratio of one magnitude to another is greater that that of a third magnitude to a fourth, when it is possible to find equi- multiples of the antecedents and equimul- tiples of the consequents, such that while the multiple of the antecedent of the first ratio is greater than, or equal to, that of its con- sequent, the multiple of the antecedent of the second ratio is not greater or is less, than that of its consequent.
Def. 55. Two ratios are said to be reciprocal when the antecedent and the ...consequent of one are the consequent and the antecedent of the other, respectively.
SYLLABUB OF PLANE GEOMETRY. .23 Theor. E. Ratios which are equal to the same ratio are equal to one another.
Prop. 23. If two ratios are equal, their reciprocal ratios are equal.
Prop. 24. Equal magnitudes have the same ratio to the same magnitude; and the same magni- tude has the same ratio to equal magnitudes.
Prop. 25. Of two unequal magnitudes, the greater has a greater ratio to a third magnitude than the less has; and the same magnitude has a greater ratio to the less of two magni- tudes than it has to the greater.
What to read after Syllabus of Plane' Geometry: (Corresponding to Euclid, book I-Vi) ; Prepared As An Introduction ...?
You can find similar books in the "Read Also" column, or choose other free books by Williams Cora Lenore to read onlineMoreLess
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