Dialogues on the First Principles of the Newtonian System, Volume 4 |
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Page 19
... the same pro- Prop . XIII . position is , That triangles between the same pa- rallels are to one another in the ratio of their bases . For into whatever number of equal parts Prop . XIV . Prop . XV . you may C 2 DIALOGUE III. ...
... the same pro- Prop . XIII . position is , That triangles between the same pa- rallels are to one another in the ratio of their bases . For into whatever number of equal parts Prop . XIV . Prop . XV . you may C 2 DIALOGUE III. ...
Page 43
... ratio all the three lines will ultimately vanish together . Does it not then appear that the ratios of lines to each other may exist and be esti- mated , independently of the lines themselves hav- ing any actual definite magnitude ? A ...
... ratio all the three lines will ultimately vanish together . Does it not then appear that the ratios of lines to each other may exist and be esti- mated , independently of the lines themselves hav- ing any actual definite magnitude ? A ...
Page 45
... bodies would fall , in the supposed indefinitely small por- tion of time , by the sole operation of the centri- petal forces , and therefore ( by Prop . XXIII . A. ) will be to each other in the ratio of those DIALOGUE VI . 45.
... bodies would fall , in the supposed indefinitely small por- tion of time , by the sole operation of the centri- petal forces , and therefore ( by Prop . XXIII . A. ) will be to each other in the ratio of those DIALOGUE VI . 45.
Page 46
... ratio they retain through all their changes ; if you mul- tiply the one always by one certain number , and the other by one other certain number , the ratio will indeed be altered , but that altered ratio will 46 DIALOGUE VI .
... ratio they retain through all their changes ; if you mul- tiply the one always by one certain number , and the other by one other certain number , the ratio will indeed be altered , but that altered ratio will 46 DIALOGUE VI .
Page 47
... ratio are taken instead of the quantities themselves . So that though the ratio existing be- tween any two quantities is not the same with the ratio between their squares ; yet , if those quantities be so augmented or diminished as al ...
... ratio are taken instead of the quantities themselves . So that though the ratio existing be- tween any two quantities is not the same with the ratio between their squares ; yet , if those quantities be so augmented or diminished as al ...
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Dialogues on the First Principles of the Newtonian System Walter Henry Burton No preview available - 2009 |
Common terms and phrases
altitude angle ABC angle ACB angle MPH arithmetical progression ascertain attraction bisect centre of gravity centripetal force circle circumference common centre curve curvilinear figure ABC definite diagonal DIALOGUE diameter difference direction divided drawn parallel ellipses equal bases exterior angle fixed point fraction greater hypothenuse indefinitely small portion instance law of motion line BD line be drawn line drawn magnitude monstration moon move multiplying number of equal number of longitudinal number of terms observed orbit parallel lines parallelogram pass perpendicular planets produced Prop proportional proportionate proposition prove quantities of matter quotient radii radius rallel ratio rectangle CD rection represented respectively equal right angles round the earth SBD is equal single impulse space square described square of CD square root straight line sun's supposed supposition thing three angles three sides tion triangle ABC uniform velocity wind XXIII
Popular passages
Page 2 - Certainly, it is heaven upon earth, to have a man's mind move in charity, rest in providence, and turn upon the poles of truth.
Page 2 - If two triangles have two sides of the one equal to two sides of the...
Page 19 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.
Page 37 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Page 2 - Euclid's, and show by construction that its truth was known to us ; to demonstrate, for example, that the angles at the base of an isosceles triangle are equal...
Page 10 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 51 - Multiply one half the sum of the first and last terms by the number of terms. Thus, the sum of eight terms of the series whose first term is 3 and last term 38 is 8 x * (3 + 38) = 164.
Page 19 - Parallelograms on the same base, and between the same parallels, are equal to one another.
Page 38 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.
Page 6 - Then, because the three angles of every triangle are together equal to two right angles, [I.