The Logic and Utility of Mathematics: With the Best Methods of Instruction Explained and Illustrated |
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Page 103
... surface or plane : hence , a plane has two dimensions , length and breadth . If now we draw a line on either side of this plane , we shall have another dimension of space , called thickness : hence , space has three Space has dimensions ...
... surface or plane : hence , a plane has two dimensions , length and breadth . If now we draw a line on either side of this plane , we shall have another dimension of space , called thickness : hence , space has three Space has dimensions ...
Page 104
... Surface : Plane , Curved . Difference . § 84. A portion of space having two dimen- sions is called a surface . There are two kinds of surfaces -- Plane Surfaces and Curved Sur- faces . With the former , a straight line , having two ...
... Surface : Plane , Curved . Difference . § 84. A portion of space having two dimen- sions is called a surface . There are two kinds of surfaces -- Plane Surfaces and Curved Sur- faces . With the former , a straight line , having two ...
Page 111
... surface , all the points of which are equally distant from a certain point within called the centre , is but a mental con- crete . ception of form ; but regarded as a solid mass , of the con- it gives rise to the additional idea of a ...
... surface , all the points of which are equally distant from a certain point within called the centre , is but a mental con- crete . ception of form ; but regarded as a solid mass , of the con- it gives rise to the additional idea of a ...
Page 141
... Surface , and Units of Solidity . UNITS OF LENGTH . Units of length . It is a § 140. The unit of length is used for measur- ing lines , either straight or curved . The stand straight line of a given length , and CHAP . II . ] 141 ...
... Surface , and Units of Solidity . UNITS OF LENGTH . Units of length . It is a § 140. The unit of length is used for measur- ing lines , either straight or curved . The stand straight line of a given length , and CHAP . II . ] 141 ...
Page 142
... SURFACE . Units of surface . § 141. Units of surface are used for the meas- urement of the area or contents of whatever has the two dimensions of length and breadth . The What the unit of surface is a square de- unit of surface is ...
... SURFACE . Units of surface . § 141. Units of surface are used for the meas- urement of the area or contents of whatever has the two dimensions of length and breadth . The What the unit of surface is a square de- unit of surface is ...
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Common terms and phrases
abstract Algebra algebraic quantity analysis Analytical Geometry applicable apprehended argument arithmetic axioms basis bers branch called combinations 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 ical idea Induction inferred integer integer units Integral Calculus kind knowledge known language laws learner length logic mathematical science means method metic middle term mind multiplied Natural Philosophy nature operations plane practical predicate premises principles properties proportion proposition pupil quantity quotient ratio reasoning regarded relation right angles scale of tens sensible objects sides signification solid square straight line subtraction surface syllogism symbols things tion triangle Troy Weight true truths unit of measure unity whole words yard
Popular passages
Page 305 - 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.
Page 235 - 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.
Page 50 - 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.
Page 1 - MATHEMATICS. The Logic and Utility of Mathematics, with the best Methods of Instruction, explained and illustrated.
Page 243 - AD c, have two sides, and the included angle of the one equal to two sides and the included angle of the other, each \ to each, and are equal in all their parts...
Page 60 - 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.
Page 73 - ... 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.