Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and ExplanatoryJohnson, 1803 - 279 páginas |
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Página 196
... section , is perpendicular to the other . 4. The inclination of a right line to a plane , is the angle it makes with another line , drawn from the point of fection , to that point in the plane , which is cut by a perpendicular falling ...
... section , is perpendicular to the other . 4. The inclination of a right line to a plane , is the angle it makes with another line , drawn from the point of fection , to that point in the plane , which is cut by a perpendicular falling ...
Página 199
... section , is perpendicular to the other . 4. The . inclination of a right line to a plane , is the angle it makes with another line , drawn from the point of fection , to that point in the plane , which is cut by a perpendicular falling ...
... section , is perpendicular to the other . 4. The . inclination of a right line to a plane , is the angle it makes with another line , drawn from the point of fection , to that point in the plane , which is cut by a perpendicular falling ...
Página 212
... section AD ; and DF in the plane CB at right angles to the common section DC ( 1. 11. ) Then because the plane AB is perpendicular to the plane ACD ( by Hyp . ) , the line DE will also be perpendi- cular to that plane ( VII . 3. ) And ...
... section AD ; and DF in the plane CB at right angles to the common section DC ( 1. 11. ) Then because the plane AB is perpendicular to the plane ACD ( by Hyp . ) , the line DE will also be perpendi- cular to that plane ( VII . 3. ) And ...
Página 226
... section KN will be parallel to the fection AD ( VII . 12. ) And fince AK is alfo parallel to DN ( VII . Def . 3. ) , the figure AN is a parallelogram ; and confequently KN is equal to AD ( I. 30. ) In like manner it may also be shewn ...
... section KN will be parallel to the fection AD ( VII . 12. ) And fince AK is alfo parallel to DN ( VII . Def . 3. ) , the figure AN is a parallelogram ; and confequently KN is equal to AD ( I. 30. ) In like manner it may also be shewn ...
Página 227
... section ABCD . Q. E. D. PROP , IX . THEOREM . Prifms of equal bafes and altitudes are equal to each other . Let AM , ES 每联 112 E be any two prifms , ftanding upon the equal bafes ABCD , EFGH , and having equal altitudes ; then will AM ...
... section ABCD . Q. E. D. PROP , IX . THEOREM . Prifms of equal bafes and altitudes are equal to each other . Let AM , ES 每联 112 E be any two prifms , ftanding upon the equal bafes ABCD , EFGH , and having equal altitudes ; then will AM ...
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Otras ediciones - Ver todas
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD abfurd alfo equal alſo be equal alternate angle altitude angle ABC angle ACB angle AGH angle BAC angle CAB angle CBD angle DEF angle EGB bafe baſe becauſe bifect centre circle ABC circumference Conft COROLL demonftrated diagonal diſtance draw equal and parallel equal to BC equiangular equimultiples EUCLID fame manner fame multiple fame parallels fame ratio fection fegment fhewn fide AB fide BC fince the angles folid fome fquares of AC given right line interfect join the points lefs leſs Let ABC Let the right magnitudes muſt oppofite angle outward angle parallel right lines parallelogram parallelogram AC perpendicular polygon Prop propofition Q.E.D. PROP rectangle of AC remaining angle right angles right lines AB ſame SCHOLIUM ſquare ſtand taken THEOREM theſe thoſe three fides triangle ABC whence
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página xii - The radius of a circle is a right line drawn from the centre to the circumference.
Página 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.
Página 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.