 EF is equal to the length of the string FGC : take away the common part FG, and the remainder EG will be equal to the remainder GC. COROLLARY. »Hence that segment of the axis which is intercepted between the focus and the directrix, is bisected in the...  Elements of the Conic Sections - Page 7by Robert Simson - 1809 - 177 pagesFull view - About this book
 | Richard Jack - Conic sections - 1742 - 378 pages
...focus, is bifected in the principal vertex of the parabola. PROPOSITION II. THEOREM II. If the diftance of any point from the focus of a parabola be equal to a line drawn from the fame point perpendicular to the line of direction, that point will be in the... | |
 | Robert Simson - Conic sections - 1775 - 306 pages
...the vertex of .the axis. Thus CB is bifected inH. PROP. II. THEOR. If the diflance of any point froni the focus of a parabola be equal to the perpendicular drawn from that point to the directrix, that fame point is in the parabola. |r;gj Let there be a parabola, the... | |
 | William Nicholson - 1809 - 716 pages
...taken aw:iy, there remains EG = G CQED The reverse of this proposition is equally evident, >/:. that 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. ч. If from a point... | |
 | William Nicholson - Natural history - 1809 - 684 pages
...taken away, there remains EG = G CQED The reverse of this proposition is equally evident, 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. •.'. If from... | |
 | Robert Simson - Conic sections - 1817 - 298 pages
...of the ruler which is on the same side of AB with the focus C : therefore EF is equal to the length of the string FGC : take away the common part FG,...point to the directrix, that point is in the parabola. F;S. i. Let there be a parabola, the directrix of which is AB, and the focus C ; and let D be a point,... | |
 | William Nicholson - Natural history - 1821 - 406 pages
...taken away, there remains EG = G CQED The reverse of this proposition is equally evident, viz. that it 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. 2. If from a point... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...curve. PROPOSITION II. In the parabola, the line drawn from the focus to any point in the curve, is equal to the perpendicular drawn from the same point to the directrix. (See last Figure.) Let P be any point in the curve, PX a perpendicular on the directrix, and F the... | |
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