## Uniplanar Algebra: Being Part I of a Prop©¡deutic to the Higher Mathematical Analysis |

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5.) Hence, by the rule of conversion, - (Def. 2, Ax. ii.) A > — or < B according as C

: A < = or > C : B. This proves the second part of each of the two propositions. (i) .

5.) Hence, by the rule of conversion, - (Def. 2, Ax. ii.) A > — or < B according as C

: A < = or > C : B. This proves the second part of each of the two propositions. (i) .

**Corollary**.• .f A : C> B : C, then C : A < C : B, and conversely. (ii) .**Corollary**. 11 ÆäÀÌÁö

Propos1t1on 9, "If two ratios be equal, and any equimultiples of the antecedents

and also of the consequents be taken, the multiple of the first antecedent has to ...

**Corollary**.- If A : B :: P : Q, «A: «B : : nP : nQ, whatever integcrs m and n may be.Propos1t1on 9, "If two ratios be equal, and any equimultiples of the antecedents

and also of the consequents be taken, the multiple of the first antecedent has to ...

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base, the segments of one side are to one another in the same ratio as the

segments of the other side." (ii) .

more ...

**Corollary**: " If the sides of a tri- F'g- 4 angle be cut by a straight line parallel to thebase, the segments of one side are to one another in the same ratio as the

segments of the other side." (ii) .

**Corollary**: " If two straight lines be cut by four ormore ...

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their bases. ' ' Propos1t1on 17. "In the same circle, or in equal circles, angles at

the cen- tre and sectors are to one another as the arcs on which they stand.

**Corollary**: " Parallelograms or triangles of the same altitude are to one another astheir bases. ' ' Propos1t1on 17. "In the same circle, or in equal circles, angles at

the cen- tre and sectors are to one another as the arcs on which they stand.

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OKA : O'K'B :: OA : O'B, (Def. 5.) wherein OKA and O'K'B represent either angles

or sectors. (i).

intercepted by common radii bear always the same ratio to one another: That is, ...

OKA : O'K'B :: OA : O'B, (Def. 5.) wherein OKA and O'K'B represent either angles

or sectors. (i).

**Corollary**: In any two given concentric circles, corresponding arcsintercepted by common radii bear always the same ratio to one another: That is, ...

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