Dialogues on the First Principles of the Newtonian System, Volume 4 |
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Page 3
... thing that is possible . B. Well then here is our isosceles triangle , Prop . II . ABC , of which the side AB is equal to the side AC . We are to prove that the angle B is also equal to the angle C. Suppose another triangle DEF , of ...
... thing that is possible . B. Well then here is our isosceles triangle , Prop . II . ABC , of which the side AB is equal to the side AC . We are to prove that the angle B is also equal to the angle C. Suppose another triangle DEF , of ...
Page 5
... thing of parallel lines . The nature of these is such , that any straight line , which meets one of them , and is in the same plane with both , will meet the other also , and will make the same angles with it as with the first , and in ...
... thing of parallel lines . The nature of these is such , that any straight line , which meets one of them , and is in the same plane with both , will meet the other also , and will make the same angles with it as with the first , and in ...
Page 7
... thing may be proved by producing one of the sides , as BC , to F , and through C drawing CG parallel to BA ; whence it also becomes evident that the exterior angle ACF , which is formed by producing BC , is equal to both the remote ...
... thing may be proved by producing one of the sides , as BC , to F , and through C drawing CG parallel to BA ; whence it also becomes evident that the exterior angle ACF , which is formed by producing BC , is equal to both the remote ...
Page 8
... things to me which seem worth knowing ; but I find myself as far from the stars as ever . B. On the contrary , you have made consider- able progress in your ascent . ascent . At At present you are under a cloud : but , when you have ...
... things to me which seem worth knowing ; but I find myself as far from the stars as ever . B. On the contrary , you have made consider- able progress in your ascent . ascent . At At present you are under a cloud : but , when you have ...
Page 9
... thing to be shewn here is , that in every parallelogram the opposite sides are equal , and also the opposite angles ; and that a straight line drawn from one angle to the opposite one ( which line we call the diagonal , or diameter ) di ...
... thing to be shewn here is , that in every parallelogram the opposite sides are equal , and also the opposite angles ; and that a straight line drawn from one angle to the opposite one ( which line we call the diagonal , or diameter ) di ...
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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.