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acceleration Assuming axes axis ball base bisected body cent centre circle coefficient common condition Conic curve DECEMBER Define described determine diameter difference direction distance Divide divisible draw drawn equal equation equilibrium Euclid expression feet focus forces four fraction gallons give given gravity half Hence inches inclined increases integration intersect Join length limiting MATHEMATICS means Multiply obtain opposite original parabola parallel parallelogram Parkinson's Mechanics particle passing perpendicular places plane positive produced Prop prove radius ratio remainder represented respectively rest Result right angles roots seconds segments shew sides signs Similarly space square straight line string Subtract tangent tension third Todhunter's Trigonometry triangle Trig unit velocity vertex vertical virtual weight whence whole number yards
Side 55 - If two triangles have two sides of the one equal to two sides of the...
Side 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Side 12 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 13 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Side 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 13 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Side 62 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
Side 13 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.