# Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory

Johnson, 1803 - 279 Seiten

### Inhalt

 Abschnitt 1 1 Abschnitt 2 7 Abschnitt 3 7 Abschnitt 4 17 Abschnitt 5 xii Abschnitt 6 xii Abschnitt 7 18 Abschnitt 8 24
 Abschnitt 20 63 Abschnitt 21 83 Abschnitt 22 90 Abschnitt 23 95 Abschnitt 24 111 Abschnitt 25 125 Abschnitt 26 189 Abschnitt 27 190

 Abschnitt 9 33 Abschnitt 10 35 Abschnitt 11 23 Abschnitt 12 24 Abschnitt 13 29 Abschnitt 14 33 Abschnitt 15 21 Abschnitt 16 25 Abschnitt 17 37 Abschnitt 18 45 Abschnitt 19 47
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### Beliebte Passagen

Seite 63 - AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Seite 31 - THE Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.
Seite xii - To find the centre of a given circle. Let ABC be the given circle ; it is required to find its centre. Draw within it any straight line AB, and bisect (I.
Seite xxiii - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Seite 63 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Seite 24 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw* the straight line GAH touching the circle in the a 17. 3. point A, and at the point A, in the straight line AH, makeb b 23.
Seite i - ELEMENTS of GEOMETRY, containing the principal Propositions in the first Six and the Eleventh and Twelfth Books of Euclid, with Critical Notes ; and an Appendix, containing various particulars relating to the higher part* of the Sciences.
Seite xii - The radius of a circle is a right line drawn from the centre to the circumference.
Seite 30 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Seite 7 - Beciprocally, when these properties exist for 'two right lines and a common secant, the two lines are parallel.* — Through a given point, to draw a right line parallel to a given right line, or cutting it at a given angle, — Equality of angles having their sides parallel and their openings placed in the same direction.