The Logic and Utility of Mathematics,: With the Best Methods of Instruction Explained and IllustratedA.S. Barnes & Burr, 1850 - 375 σελίδες |
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Σελίδα 6
... .. 54-61 Distribution and Non - distribution of Terms . 61-67 Rules for examining Syllogisms .... 67 Of Fallacies .... 68-71 Concluding Remarks . 71-75 BOOK II . MATHEMATICAL SCIENCE . CHAPTER I. QUANTITY AND 6 CONTENTS .
... .. 54-61 Distribution and Non - distribution of Terms . 61-67 Rules for examining Syllogisms .... 67 Of Fallacies .... 68-71 Concluding Remarks . 71-75 BOOK II . MATHEMATICAL SCIENCE . CHAPTER I. QUANTITY AND 6 CONTENTS .
Σελίδα 7
... QUANTITY AND MATHEMATICAL SCIENCE DEFINED DIFFER- ENT KINDS OF QUANTITY - LANGUAGE OF MATHEMATICS EXPLAINED - SUBJECTS CLASSIFIED - UNIT OF MEASURE DEFINED MATHEMATICS A DEDUCTIVE SCIENCE .... Page - Quantity Number . 99 SECTION Space ...
... QUANTITY AND MATHEMATICAL SCIENCE DEFINED DIFFER- ENT KINDS OF QUANTITY - LANGUAGE OF MATHEMATICS EXPLAINED - SUBJECTS CLASSIFIED - UNIT OF MEASURE DEFINED MATHEMATICS A DEDUCTIVE SCIENCE .... Page - Quantity Number . 99 SECTION Space ...
Σελίδα 18
... quantities Number and Space , it appeared indispensable to give , in a manner best adapted to my purpose , an out- line of the nature of that reasoning by means of which all inferred knowledge is acquired . Book II . Of what it treats ...
... quantities Number and Space , it appeared indispensable to give , in a manner best adapted to my purpose , an out- line of the nature of that reasoning by means of which all inferred knowledge is acquired . Book II . Of what it treats ...
Σελίδα 21
... quantities Number and Space . mathematics . the results . When the professional student shall have ex- amined the subject , even to the extent to which Certainty of it is here treated , he will be impressed with the clearness ...
... quantities Number and Space . mathematics . the results . When the professional student shall have ex- amined the subject , even to the extent to which Certainty of it is here treated , he will be impressed with the clearness ...
Σελίδα 26
... quantity — and this is the logic of mathematics . If he would accom- Results of plish well his work , he must so instruct his pupils that they shall apprehend clearly , think quickly and correctly , reason justly , and open their minds ...
... quantity — and this is the logic of mathematics . If he would accom- Results of plish well his work , he must so instruct his pupils that they shall apprehend clearly , think quickly and correctly , reason justly , and open their minds ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abstract affirmed Algebra algebraic quantity analysis Analytical Geometry applicable apprehended argument arithmetic axioms basis bers branch called common compared conclusion connection copula Croton aqueduct curved deductive deductive reasoning defined definition denominate numbers Descriptive Geometry divided division elementary employed ence equal equation eral example explained expressed facts feet figures frac fractional units geometrical magnitudes gism Hence idea Induction inferred integer integer units Integral Calculus kind knowledge known language laws learner length logic mathematical science means ment method metic middle term mind multiplied Natural Philosophy nature notions operations plane practical predicate premises principles properties proportion proposition pupil quantity quotient ratio reasoning regarded relation right angles rules scale of tens sides signification solid square straight line subtraction surface syllogism symbols things tion triangle Troy Weight true truths unit of measure unity whole words yard
Δημοφιλή αποσπάσματα
Σελίδα 233 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 303 - In the mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it ; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Σελίδα 315 - Admission to its sanctuary, and to the privileges and feelings of a- votary, is only to be gained by one means — sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Σελίδα 48 - Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
Σελίδα 283 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Σελίδα 58 - IN every instance in which we reason, in the strict sense of the word, ie make use of arguments, whether for the sake of refuting an adversary, or of conveying instruction, or of satisfying our own minds on any point, whatever may be the subject we are engaged on, a certain process takes place in the mind, which is one and the same in all cases, provided it be correctly conducted.
Σελίδα 65 - the trees flourish, because the ground is rich," or " the ground is rich, and therefore the trees flourish," I am using the very same conjunctions to denote the connection of cause and effect ; for in this case, the luxuriance of the trees, being evident to the eye, would hardly need to be proved, but might need to be accounted for.
Σελίδα 247 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 241 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 71 - ... whatever is predicated (ie affirmed or denied) universally, of any class of things, may be predicated, in like manner, (viz. affirmed or denied) of any thing comprehended in that class.