Universal Arithmetick: Or, A Treatise of Arithmetical Composition and Resolution, Volume 1

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W. Johnston, 1769 - Algebra - 599 pages
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Page 46 - 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...
Page 46 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.
Page 204 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.
Page 201 - Parts may be exprejjed 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 fhall accommodate them, to Computation.
Page 181 - 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.
Page 40 - The total number of decimal places in the product is the sum of the number of places (to the right of the decimal point) in all of the numbers multiplied.
Page 47 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth. The...
Page 388 - ... two of the roots; that of the fourth, if its sign be changed, is equal to the aggregate of the contents under each three of the roots, that of the fifth is equal to the aggregate of the contents each four, and so on ad infinitum".
Page 170 - Produńs of the oppofite Coefficients taken from the Orders that involve the two unknown Quantities. (Coefficients are of the...
Page 108 - 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...

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