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

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... two 0i them can be true at the same time), then the converse of every theorem

of the group will necessarily be true." {Syllabus of Plane Geometry, p. 5.)

incommensurable if no such

INTRODUCTION.

... two 0i them can be true at the same time), then the converse of every theorem

of the group will necessarily be true." {Syllabus of Plane Geometry, p. 5.)

incommensurable if no such

**coincidence**takes place, however far the 4INTRODUCTION.

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incommensurable if no such

comparison is carried. 5. The ratio of two magnitudes is said to be equal to a

second ratio of two other magnitudes (whether of the same or of a different kind

from ...

incommensurable if no such

**coincidence**takes place, however far the process ofcomparison is carried. 5. The ratio of two magnitudes is said to be equal to a

second ratio of two other magnitudes (whether of the same or of a different kind

from ...

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...

sufficiently the aggregate of all the spaces between the arcs and their chords may

be made smaller than any previously assigned arbitrarily small magnitude. Under

these ...

...

**coincidence**with the arcs S and S' respectively ; and by increasing msufficiently the aggregate of all the spaces between the arcs and their chords may

be made smaller than any previously assigned arbitrarily small magnitude. Under

these ...

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Take P, Q, R, on the same line, A Q B H P ' . a b Fig. 12. such that AP=/AQ = /a,

BP=/BP = /b, and let Q pass into

range, R passes into

OPERATION.

Take P, Q, R, on the same line, A Q B H P ' . a b Fig. 12. such that AP=/AQ = /a,

BP=/BP = /b, and let Q pass into

**coincidence**with A. P then passes out of finiterange, R passes into

**coincidence**with B and LAWS OF ALGEBRAICOPERATION.

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Being Part I of a Prop©¡deutic to the Higher Mathematical Analysis Irving

Stringham. of finite range, R passes into

AB = / a — / b, whatever its original value, assumes the form / o — / O 00 — 00.

Hence ...

Being Part I of a Prop©¡deutic to the Higher Mathematical Analysis Irving

Stringham. of finite range, R passes into

**coincidence**with B and the differenceAB = / a — / b, whatever its original value, assumes the form / o — / O 00 — 00.

Hence ...

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