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Books Books 1 - 10 of 10 on B, according as mP is greater than, equal to, or less than Q, whatever whole numbers....
" B, according as mP is greater than, equal to, or less than Q, whatever whole numbers m and n may be. It is an immediate consequence that: The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and... "
Uniplanar Algebra: Being Part I of a Propdeutic to the Higher Mathematical ... - Page 5
by Irving Stringham - 1893 - 141 pages
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SYLLABUS OF PLANE GEOMETRY

1876
...other antecedent is greater than, equal to, or less than that of its consequent. Or in other words : The ratio of A to B is equal to that of P to Q,,when wA is greater than, equal to, or less than ?zB, according as mP is greater than, equal to or...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

1878 - 372 pages
...And then follows as an "immediate consequence" its application to incommensurable magnitudes : — The ratio of A to B is equal to that of P to Q, when, m being any number whatever, and n another number determined so that m A is between n B and (n...
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Elementary Geometry, Books 1-5

James Maurice Wilson - Geometry - 1878 - 261 pages
...to, or less than Q, whatever whole numbers m and may be. It is an immediate consequence that : The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and another number determined so that either aA is between...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878
...1. Four magnitudes, A and B of one kind, and C and D of the same or another kind, are proportional, when the ratio of A to B is equal to that of C to D ; that is, when TJ. = :pr (II., 7). Thus A and B may be two lines, C and D, two triangles. The...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid ..., Books 1-6

Mathematical association - 1883
...equal to, or less than Q, whatever whole numbers m and n may be. It is an immediate consequence that: The ratio of A to B is equal to that of P to Q ; when, m being any number whatever, and another number determined so that either /A is between...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching, Euclid - Euclid's Elements - 1888
...equal to, or less than wQ, whatever whole numbers m and n may be. It is an immediate consequence that : The ratio of A to B is equal to that of P to Q, when, m being any number whatever, and another number determined so that either mA. is between B...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Randal Charles John Nixon - Geometry - 1890 - 400 pages
...between them. Euclid's definition, expressed in the notation already indicated, is the same as this — The ratio of A to B is equal to that of P to Q when m A >, =, or < n B according as mP >, =, or < nQ, whatever numbers m and n may be. It is an immediate...
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The Elements of Euclid: Viz. the First Six Books, Together with the ..., Book 11

Euclid, Robert Simson - Geometry - 1892 - 518 pages
...distributed among those of B in the same manner as the multiples of C are distributed among those of D. 5. When the ratio of A to B is equal to that of C to D the four magnitudes are called proportionals. This is ex' presjied by saying " A is to B as...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid, H. S. Hall, F. H. Stevens - Euclid's Elements - 1904 - 456 pages
...proportion, when the ratio of the first to the second is equal to the ratio of the third to the fourth. When the ratio of a to b is equal to that of x to y, the four magnitudes are called proportionals. This is expressed by saying " a is to b as x...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - Geometry - 1905 - 42 pages
...order as the multiples of the antecedent of the second ratio among those of its consequent. Def. 53. When the ratio of A to B is equal to that of P to Q the four magnitudes, A, B, P, Q, are said to be proportionals, or to form a proportion. The proportion is denoted thus:...
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