COMMANDINE (Frederick)

, a celebrated mathematician and linguist, was born at Urbino in Italy, in 1509; and died in 1575; consequently at 66 years of age. He was famous for his learning and knowledge in the sciences. To a great depth, and just taste in the mathematics, he joined a critical skill in the Greek language; a happy conjunction which made him very well qualified for translating and expounding the writings of the Greek mathematicians. And accordingly, with a most laudable zeal and industry, he translated and published several of their works, to which no former writer had done that good office. On which account, Francis Moria, duke of Urbino, who was very conversant in those sciences, proved a very affectionate patron to him. He is greatly applauded by Bianchanus, and other writers; and he justly deserved their encomiums.

Of his own works Commandine published the following:

1. Commentarius in Planisphærium Ptolomæi: 1558, in 4to.

2. De Centro Gravitatis Solidorum: Bonon. 1565, in 4to.

3. Horologiorum Descriptio: Rom. 1562, in 4to.

He translated and illustrated with notes the following works, most of them beautifully printed, in 4to. by the celebrated printer Aldus:

1. Archimedis Circuli Dimensio; de Lineis Spiralibus; Quadratura Parabolæ; de Conoidibus & Sphæroidibus; de Arenæ Numero: 1558.

2. Ptolomæi Planisphærium; & Planisphærium Jordani: 1558.

3. Ptolomæi Analemma: 1562.

4. Archimedis de iis quæ vehuntur in aqua: 1565.

5. Apollonii Pergæi Conicorum libri quatuor, una cum Pappi Alexandrini Lemmatibus, & Commentariis Eutocii Ascalonitæ, &c: 1566.

6. Machometes Bagdadinus de Superficierum Divisionibus: 1570.

7. Elementa Euclidis: 1572.

8. Aristarchus de Magnitudinibus & Distantiis Solis & Lunæ: 1572.

9. Heronis Alexandrini Spiritualium liber: 1583:

10. Pappi Alexandrini Collectiones Mathematicæ: 1588.

COMMANDING Ground, in Fortification, an eminence, or rising ground, overlooking any post or strong place. This is of three sorts. 1st, A Front Commanding Ground, or a height opposite to the face of the post, which plays upon its front. 2dly, A Reverse Commanding Ground, or an eminence that can play upon the rear or back of the post. 3dly, An Enfilade Commanding Ground, or an eminence in flank which can, with its shot, scour all the length of a straight line.

COMMENSURABLE Quantities, or Magnitudes, are such as have some common aliquot part, or which may be measured or divided, without a remainder, by one and the same measure or divisor, called their common measure. Thus, a foot and a yard are commensurable, because there is a third quantity that can measure each, viz an inch; which is 12 times contained in the foot, and 36 times in the yard.—Commensurables are to each other, as one rational whole number is to another; but incommensurables are not so: And therefore the ratio of commensurables is rational; but that of incommensurables, irrational: hence also the exponent of the ratio of commensurables, is a rational number.

COMMENSURABLE Numbers, whether integers, or fractions, or surds, are such as have some other number, which will measure or divide them exactly, or without a remainder. Thus, 6 and 8 are-commensurable, because 2 measures or divides them both. And 2/3 and 3/4, or 8/12 and 9/12 are commensurable fractions, because the fraction 1/6, or 1/12, &c, will measure them both: and in this sense, all fractions may be said to be commensurable. Also, the surds 2√2 and 3√2 are commensurable, being measured by √2, or being to each other as 2 to 3.

Commensurable in Power. Euclid says, right lines are commensurable in power, when their squares are measured by one and the same space or superficies.