## Outlines of geometry; or, The motion of a point |

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already angle appear ascertained axis becomes breadth calculated called centre CHAPTER circle circular co-ordinates common conceived condition consequently considered contained continued course curve decrease definite depends described determine difficulty direction distance drawn enclosed equal equation Euclid evident examine example existence expressed fact figure fixed former further geometrical Geometry give given gradually Hence idea increase infinite infinitesimal kind known latter length less limit locus magnitude manner Mathematics means measure merely method miles motion moving nature object observed obtained once opposite orbit parallel particular pass path perhaps plane position possible present principle problem proposition proved question radius regard relation remains represents revolving right angles round seen sides similar solid space storm straight line student Suppose surface tangent third three points trace treatise triangle various vary whole wind zero

### Popular passages

Page 52 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 23 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 26 - A segment of a circle is the figure contained by a straight line and the circumference it cuts off.

Page 29 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of these angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 21 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 51 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.

Page 51 - Let BAC be the given rectilineal angle, it is required to bisect it. Take any point D in AB, and from AC cut (i.

Page 41 - all right angles (for example) are equal to one another ; " that " when one straight line falling on two other straight lines makes the two interior angles on the same side less than two right angles, these two straight lines, if produced, shall meet on the side, where are the two angles less than two right angles ; " are manifestly principles which bear no analogy to such barren truisms as these, " Things that are equal to one and the same thing are equal to one another.

Page 80 - ... but the wind drew round and round, according to the now known laws of these circular storms, and she, with a perseverance that might have been more wisely employed, continued to scud " right before it " for four successive days and nights, by which time she had actually circumnavigated the storm-field five times.

Page 22 - And that a circle may be described from any centre, at any distance from that centre.