## Dialogues on the First Principles of the Newtonian System, Volume 4 (Google eBook) |

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### Common terms and phrases

altitude angle ABC angle ACB angle MPH arithmetical progression ascertain attraction bisect centre of gravity centripetal force circle circumference coincide in position common centre curve curvilinear figure ABC definite diagonal DIALOGUE diameter difference direction divided drawn parallel ellipses equal bases fixed point fraction greater hypothenuse indefinitely small portion instance isosceles triangle 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 SBC 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

### 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.