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 Induction
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acting added angles appears arising Axiom axis balance base body Book called center of gravity column common considered containing definition described destroy difference direction divided draw drawn effect equal equilibrium exerted expressed facts falling fixed fluid force forces acting fraction fulcrum Geometry given greater heavy Hence HISTORY horizontal idea increase Inductive length less lever magnitude manner mathematical matter means Mechanics motion move multiplied nature opposite parallel particles pass perpendicular plane portions position pressure principles prism produce Prop proportion proposition proved quantity ratio reasoning reference represented respectively rest rigid round sides space specific gravity straight line string supported supposed surface taken tions triangle truth tube turn uniform upwards velocity vertical weight whole
Page 22 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. 5. The inclination of a straight line to a plane...
Page 9 - Sacred History, from the Creation of the World to the Destruction of Jerusalem. With Questions for Examination.
Page 18 - ... if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth.
Page 47 - There is an equilibrium upon the wheel and axle when the power is to the weight as the radius of the axle to the radius of the wheel.
Page 20 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Page 97 - ... gravity of the fluid : the specific gravity of the body. Prop. 10. To describe the hydrostatic balance, and to shew how to find the specific gravity of a body by means of it, 1st, when its specific gravity is greater than that of the fluid in which it is weighed ; 2ndly, when it is less.