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Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914. Excerpt: ... General Axioms 1. =ty Ax. Things equal to the same thing or equal things are equal to each other. 2. Add Ax. If equals are added to the same thing or to equals, the sums are equal. 3. Sub Ax. If equals are subtracted from the same thing or from equals, the remainders are equal. 4. Mul Ax. If equals are multiplied by the same thing or by equals, the products are equal. 5. Div Ax. If equals are divided by the same thing except zero, or by equals, the quotients are equal. 6. In = ity Ax Add. If unequals are added to the same thing or to equals, the sums are unequal and the greater sum is the one to which the greater addition is made. 7. In = ity Ax Sub. If unequals are subtracted from the same thing or from equals, the remainders are unequal and the greater remainder is the one from which the lesser subtraction is made. 8. In = ity Ax Mul. If unequals are multiplied by the same thing or by equals, the products are unequal and the greater product is the one obtained from the greater multiplicand. 9. In = ity Ax Div. If unequals are divided by the same thing or by equals, the quotients are unequal and the greater quotient is the one obtained from the greater dividend. 10. Sum Pts Ax. The whole equals the sum of its parts and is therefore greater than any of its parts when all are positive. 11. Power and Root Ax. Like powers and like roots of equals are equal. 12. Frac Ax. If both numerator and denominator of a fraction are multiplied or divided by the same thing, the value of the fraction is unchanged. 13. Subs Ax (Substitution Axiom). A quantity may be substituted for its equal, in any equation or inequality, without affecting the relation of the members. Geometric Axioms 14. Bet 2 Pts 1 St. Only one straight line can be drawn between two points. Two straigh...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914. Excerpt: ... General Axioms 1. =ty Ax. Things equal to the same thing or equal things are equal to each other. 2. Add Ax. If equals are added to the same thing or to equals, the sums are equal. 3. Sub Ax. If equals are subtracted from the same thing or from equals, the remainders are equal. 4. Mul Ax. If equals are multiplied by the same thing or by equals, the products are equal. 5. Div Ax. If equals are divided by the same thing except zero, or by equals, the quotients are equal. 6. In = ity Ax Add. If unequals are added to the same thing or to equals, the sums are unequal and the greater sum is the one to which the greater addition is made. 7. In = ity Ax Sub. If unequals are subtracted from the same thing or from equals, the remainders are unequal and the greater remainder is the one from which the lesser subtraction is made. 8. In = ity Ax Mul. If unequals are multiplied by the same thing or by equals, the products are unequal and the greater product is the one obtained from the greater multiplicand. 9. In = ity Ax Div. If unequals are divided by the same thing or by equals, the quotients are unequal and the greater quotient is the one obtained from the greater dividend. 10. Sum Pts Ax. The whole equals the sum of its parts and is therefore greater than any of its parts when all are positive. 11. Power and Root Ax. Like powers and like roots of equals are equal. 12. Frac Ax. If both numerator and denominator of a fraction are multiplied or divided by the same thing, the value of the fraction is unchanged. 13. Subs Ax (Substitution Axiom). A quantity may be substituted for its equal, in any equation or inequality, without affecting the relation of the members. Geometric Axioms 14. Bet 2 Pts 1 St. Only one straight line can be drawn between two points. Two straigh...
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