Page:First six books of the elements of Euclid 1847 Byrne.djvu/31

Rh SYMBOLS AND ABBREVIATIONS.

&#8756; expresses the word therefore.

&#8757; . . . . . . . . . . . . . . . . because.

= . . . . . . . . . . . . . . . . equal. This sign of equality may be read equal to, or is equal to, or are equal to; but any discrepancy in regard to the introduction of the auxiliary verbs is, are, &c. cannot affect the geometrical rigour. &#8800; means the same as if the words  'not equal'  were written. &gt; signifies greater than.

&lt;. . . . . . less than. &#8815; . . . . . . not greater than.

&#8814; . . . . . . not less than.

+ is read plus (more), the sign of addition; when interposed between two or more magnitudes, signifies their sum.

&minus; is read minus (less), signifies subtraction; and when placed between two quantities denotes that the latter is to be taken from the former. &times; this sign expresses the product of two or more numbers when placed between them in arithmetic and algebra; but in geometry it is generally used to express a rectangle, when placed between "two straight lines which contain one of its right angles." A rectangle may also be represented by placing a point between two of its conterminous sides. : :: : expresses an analogy or proportion; thus, if A, B, C and D, represent four magnitudes, and A has to B the same ratio that C has to D, the proposition is thus briefly written,

$A : B :: C : D$, $A : B = C : D,$

or $\frac{A}{B} = \frac{C}{D}$.

This equality or sameness of ratio is read,