The Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics Demonstrated After the Manner of the Elements of Geometry; and Including the Propositions Fixed Upon by the University of Cambridge as Requisite for the Degree of B.A. To which are Added Remarks on Mathematical Reasoning and on the Logic of InductionFor J. and J.J. Deighton, 1837 - 182 σελίδες |
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The Mechanical Euclid, Containing the Elements of Mechanics and Hydrostatics ... William Whewell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
The Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics ... William Whewell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD Accelerating Force act perpendicularly algebraical algebraical quantities axis body falling body moving center of gravity column of fluid deductive Deductive Reasoning definition denominator effect equilibrium exerted fluid displaced force Q forces acting fore fraction fulcrum geometric progression Geometry heavy fluid Hence horizontal plane Hydrostatics idea immersed inclined plane INDUCTIVE PRINCIPLE Lemma magnitude manner mathematical mercury moveable multiplied Octavo P's velocity parallel parallelogram particles perpendicular piston portions position pressure upwards prism produce Prop proportion proposition pully ratio reasoning represent rest right angles rigid sides space described specific gravity straight line string supposed surface pressed tend to turn tion triangle truth tube uniform force University of Cambridge upper surface valve velocity acquired vertical column vertical line weight
Δημοφιλή αποσπάσματα
Σελίδα 91 - have two angles of the one equal to two angles of the other ; and the side KL is equal to LM. Therefore the triangles are equal, and HL is equal to MN; that is, to RS. In the same manner it may be shewn that OQ is equal to
Σελίδα 18 - ab = a*. 41. If the product of two quantities be equal to the product of two others, the four are proportionals, making the terms of one product the means, and the terms of the other the extremes. Let xy = ab, then dividing by ay,
Σελίδα 29 - tionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle. *PROP. in. If the angle of a triangle be divided by a straight line cutting the base, the segments of the base shall have the same ratio as the other side of the triangle; and if the segments of the base
Σελίδα 17 - aa ax be * (9). Algebraical definition of Proportion. 37. Four quantities are said to be proportionals, when the first is the same multiple, part, or parts of the second, that the third is of the fourth. Thus the four quantities 8. 12, 6, 9, are proportionals ; for 8 is
Σελίδα 18 - b :: c : d being given, the fourth may be determined from the equation ad = be. 40. If the first be to the second as the second to the third, the product of the extremes is equal to the square of the mean. For (Art. 39) if a
Σελίδα 18 - 39. When four quantities are proportionals, the product of the extremes is equal to the product of the means. Let a, b, c, d be the four quantities ; then, since they are proportionals. = - ; and by multiplying both sides