Traité methodique et abregé de toutes les mathematiqves

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Δημοφιλή αποσπάσματα

Σελίδα 55 - Ratiunculas are to be fo underftood as in a continued Scale of Proportionals, infinite in Number between the two Terms of the Ratio ; which infinite Number of mean Proportionals is to that infinite Number of the like and equal...
Σελίδα 203 - Parts may be exprejfed -without the Intervention of Surds, by Addition and Subtraction only. Thus, if the Perpendicular of a plane Triangle is fought, from the three Sides given ; 'tis better to fubftitute for the Segments LXXXVIII. But when you have compared the Terms of the Queftion thus generally, there is more Art and Invention required to find out the particular Connexions or Relations of the Lines that (hall accommodate them to Computation.
Σελίδα 410 - ... the coefficient of the third term is the sum of the products of every two...
Σελίδα 395 - Since the sum of the roots is equal to the sum of the elements in the main diagonal, i>,;.
Σελίδα 183 - If the Sun moves every Day one Degree, and the Moon thirteen, and at a certain Time the Sun be at the Beginning of Cancer, and in three Days after the Moon in the Beginning of Aries, the Place of their next following Conjunction is required ? 67.
Σελίδα 478 - Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists.
Σελίδα 172 - Produñs of the oppofite Coefficients taken from the Orders that involve the two unknown Quantities. (Coefficients are of the...
Σελίδα 110 - After the fame manner, the cube root of a'+x' will be found to be § 56. " The general Theorem which we gave for the Involution of binomials will ferve alfo for their Evolution ;" becaufe to extract any root of a given quantity is the fame thing as to raife that quantity to a power whofe exponent is a fraction that has...
Σελίδα 191 - ... on supposition that the grass did not grow. "But since by reason of the growth of the grass 21 oxen in 9 weeks can eat up only 10 acres, that growth of the grass...
Σελίδα 478 - Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others.

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