EXPLANATION OF CHARACTERS. Numbers found in a parenthesis refer to articles, where the proposition is demonstrated that is there relied upon. Signifies equality, or equal to; as 100 cents=one dollar; that is, 100 cents are equal to one dollar. +Signifies plus, or Addition; as 50+50=100; that is, 50 added to 50 is equal to 100. Signifies minus, or Subtraction; as 6-2=4; that is, 6 less 2 is equal to 4. × Signifies Multiplication; as 4x4-16; that is, 4 multiplied by 4 is equal to 16. When placed over a figure, shows that it does not form a part of the true result. · Signifies, when placed between two figures, their Arithmetical Ratio; thus 15 8 signifies the arithmetical ratio of 15 to 8. : Signifies the Geometrical Ratio between two numbers; thus 12 3, signifies the geometrical ratio of 12 to 3. Signifies a Continued Proportion, which is Arithmetical, or Geometrical, according as the Character between the Terms denotes; thus, 37 11 signifies an Arithmetical, and 5:20: 80, a Geometrical, Continued Proportion. Signifies an Arithmetical, or Geometrical Progression, according as the Character between the Terms denotes; thus, 2:4:8:16: &c. signifies a Geometrical progression, and 3 5 7 9, &c. an Arithmet ical progression. CONTENTS. Addition of whole Numbers and Decimals, Subtraction of whole Numbers and Decimals, Page. From the Committee, appointed by the Trustees of Gardiner Lyceum to examine this Arithmetic, previous to its introduction as a Text-Book at the Lyceum. Having examined, with some attention, the Arithmetic of Bezout, we do not hesitate to say, that, in our opinion, it contains a very lucid explanation of the principles of this important part of Mathematics, and we hope that its introduction to our Schools will make the study of Arithmetic something more than a mere exertion of memory in committing rules, and a mechanical conformity to them. The translation is faithfully and correctly made, and the Translator has added many examples to the original work, which, although we have not examined them we hope, will be found to enhance its value. BENJAMIN HALE, Principal of Gardiner Lyceum. R. H. GARDINER, Committee of Trustees. JOHN MERRICK, Gardiner, Nov. 1824. Extract of a letter to the Translator, from PARker CLEAVELAND, L. L. D. Professor of Mathemat= ics and Natural Philosophy in Bowdoin College. To NATHANIEL HAYNES, A. B. SIR, I am happy to learn that you are about giving to the Public a translation of the excellent Arithmetic of Bezout's, accompanied by "numerous select Examples, showing the application of abstract principles to a great variety of questions in business." It has long been perceived, that most of the Elementary treatises on Arithmetic are very deficient, by not containing rigorous and perspicuous demonstrations of the cominon rules of Arithmetic. The progress of the student in Mathematics is hereby much retarded, or he is even made to dislike the science. Nothing less rigorous than Bezout will supply the deficiency. I am Sir, Yours, &c. Brunswick, Nov. 1, 1824. P. CLEAVELAND. |