## Elements of Natural Philosophy, Part 1 |

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Page 3

... general varies ; and , at the same time , the plane in which the curvature lies is

through which the tangent has

... general varies ; and , at the same time , the plane in which the curvature lies is

**turning**about the tangent to the curve . ... an arc of a plane curve , is the anglethrough which the tangent has

**turned**as we pass from one extremity to the other . Page 15

SZ is perpendicular to the direction of motion PY , and thus the circular locus of Z

is the hodograph

APB be a parabola , ÀY is a straight line . But if another point U be taken in YS ...

SZ is perpendicular to the direction of motion PY , and thus the circular locus of Z

is the hodograph

**turned**through a right angle about S in the plane of the orbit . IfAPB be a parabola , ÀY is a straight line . But if another point U be taken in YS ...

Page 16

... which a planet receives heat and light from the sun varies in simple proportion

to the angular velocity of the radius - vector . Hence the whole heat and light

received by the planet in any time is proportional to the whole angle

through ...

... which a planet receives heat and light from the sun varies in simple proportion

to the angular velocity of the radius - vector . Hence the whole heat and light

received by the planet in any time is proportional to the whole angle

**turned**through ...

Page 17

Hence the arc of Pl , described in any time , is proportional to the corresponding

angle - vector in the orbit , i.e. to the angle through which the tangent to PQ has

Hence the arc of Pl , described in any time , is proportional to the corresponding

angle - vector in the orbit , i.e. to the angle through which the tangent to PQ has

**turned**. Hence ( § 9 ) the curvature of PQ is constant , or PQ is a circle . Page 18

Hence B's path about A is A's about B

regard to G and G ' it is evident that the directions remain the same , while the

lengths are altered in a given ratio ; but this is the definition of similar curves . 66.

Hence B's path about A is A's about B

**turned**through two right angles . And withregard to G and G ' it is evident that the directions remain the same , while the

lengths are altered in a given ratio ; but this is the definition of similar curves . 66.

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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently experience expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire