## Elements of Conic Sections: In Three Books: in which are Demonstrated the Principal Properties of the Parabola, Ellipse, and Hyperbola. By Richard Jack, ... |

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Elements of Conic Sections: In Three Books: in Which Are Demonstrated the ... Richard Jack No preview available - 2019 |

Elements of Conic Sections in Three Books: In Which are Demonstrated the ... Richard Jack No preview available - 2018 |

### Common terms and phrases

abfcifs abfurd alfo alſo ameter angle contained baſe bifected cauſe circle confequently conjugate diameters conjugate hyperbolas contained between AC cut the line cut the periphery cutting plane demonftrated diame directrix diſtance draw drawn parallel drawn perpendicular ellipfe equal fame diameter fame manner fame point fecond axis fecond diameter fegments femi-ordinate fide fimilar firſt fmaller foci focus fore fquare of AC fquares defcribed given line given point given right line greater axis intercepted interfection latus rectum line be drawn meter oppofite hyperbolas ordinate paffing parabola parallelogram perbola point F point of contact principal vertex PROPOSITION ptotes rallel rect rectangle contained right angles right line drawn ſquare tained tangent thefe THEOREM theſe tranf tranfverfe axis tranfverfe diameter tranſverſe triangle tween vertex wherefore

### Popular passages

Page 142 - If a tangent to the ellipse meet the transverse axis produced, and from the point of contact an ordinate be drawn to the same axis ; then is the semitransverse axis a mean proportional between the distances from the centre to the intersections of the axis by the ordinate and tangent. That is, (Fig.

Page 5 - Hz. tint if the distance of any point from the focus of a parabola, be equal > to the perpendicular drawn from it to the directrix, then shall that point fall in the curve of the parabola. Prop.

Page 62 - CD is common, the two sides AC, CD are equal to the two sides BC, CD; and the angle ACD is equal to the angle BCD, for each is right ; therefore the base AD is equal to the base DB. [i. 4] But equal straight lines cut...

Page 151 - The fum of the fquares of' any two conjugate diameters is equal to the fum of the fquares of the two axes.

Page 77 - C, and if the pin be moved round from any point until it return to tlîe place from whence it began to move, the thread being extended during the whole time of the revolution, the figure which the fmall pin by this revolution defcribes is called an ellipfe.

Page 29 - FCK is a right d. 47 i . angle, the fquare of FK is equal d to the fquares of FC, CK. for the fame reafon the fquare of FK is equal to the fquares of FB, BK. therefore the fquares of FC, CK are equal to the fquares of FB, BK, of which the fquare of FC is equal to the fquare of FB ; the remaining fquare of CK is therefore equal to the remaining fquare of BK, and e.

Page 1 - DEF a fquare, which let be placed in the fame plane in which the right line and point are., in fuch a manner that one fide of it, as...

Page 1 - EF, and the other extremity of it at the point C, and let part of the thread, as FG, be brought clofe to the...

Page 77 - ... extended by means of a fmall pin C, and if the pin be moved round from^ any point until it return to...

Page 129 - Line touches a Circle, and from the Point of Contact a Line be drawn perpendicular to the touching Line, the Center of the Circle ihall be in that Line.