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

SYMBOLS AND ABBREVIATIONS.

$\therefore$ expreſſes the word therefore.

$\because$ . . . . . . . . . . . . . . . . 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 introduƈtion of the auxiliary verbs is, are, &c. cannot affeƈt the geometrical rigour.

$\neq$ means the ſame as if the words 'not equal' were written.

$\sqsubset$ ſignifies greater than.

$\sqsupset$ . . . . . . leſs than.

$\not \sqsubset$ . . . . . . not greater than.

$\not \sqsupset$ . . . . . . not leſs than.

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

$-$ is read minus (leſs), ſignifies ſubtraƈtion; and when placed between two quantities denotes that the latter is to be taken from the former.

$\times$ this ſign expreſſes the produƈt of two or more numbers when placed between them in arithmetic and algebra; but in geometry it is generally uſed to expreſs a reƈtangle, when placed between "two ſtraight lines which contain one of its right angles." A reƈtangle 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,