## Elements of Natural Philosophy |

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Page 41

It is to be understood here , that as the radi of curvature have been considered

positive when both

either radius when the corresponding

It is to be understood here , that as the radi of curvature have been considered

positive when both

**surfaces**are convex , the negative sign must be introduced foreither radius when the corresponding

**surface**is concave . Hence the angular ... Page 42

Let P , o be two points of a

radius of curvature of a normal section passing through them . Then the radius of

curvature of an oblique section through the same points , inclined to the former ...

Let P , o be two points of a

**surface**indefinitely near to each other , and let r be theradius of curvature of a normal section passing through them . Then the radius of

curvature of an oblique section through the same points , inclined to the former ...

Page 43

The flexure of an inextensible

been well worked by geometrical investigators and writers , and , in its elements

at least , presents little difficulty . The first elementary conception to be formed is ...

The flexure of an inextensible

**surface**which can be plane , is a subject which hasbeen well worked by geometrical investigators and writers , and , in its elements

at least , presents little difficulty . The first elementary conception to be formed is ...

Page 44

There is still no difficulty in understanding the form of , säý a square , or circle , of

the plane

any of these points of intersection . When the number is infinite , and the

There is still no difficulty in understanding the form of , säý a square , or circle , of

the plane

**surface**when bent as explained above , provided it does not includeany of these points of intersection . When the number is infinite , and the

**surface**... Page 45

Hence , also , similar figures , whether constituted by actual portions of the

substance , or mere geometrical

that an ellipse remains an ellipse ; and an ellipsoid remains a

every ...

Hence , also , similar figures , whether constituted by actual portions of the

substance , or mere geometrical

**surfaces**, or ... Hence , and from $ 139 , we seethat an ellipse remains an ellipse ; and an ellipsoid remains a

**surface**of whichevery ...

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### Common terms and phrases

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 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 period perpendicular plane portion position potential practical pressure principle produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire