## The Elements of Descriptive Geometry ... |

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Página 2

( 12 ) A solid angle is trihedral , tetrahedral , pentahedral , & c . , according as it is

contained by three , four , or five , & c . , faces .

straight line cannot be in a plane , and the other part above it . If possible , let a B

...

( 12 ) A solid angle is trihedral , tetrahedral , pentahedral , & c . , according as it is

contained by three , four , or five , & c . , faces .

**PROPOSITION**I . One part of astraight line cannot be in a plane , and the other part above it . If possible , let a B

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Página 4

To prove this

drawn from B , in the plane mn . Produce AB to ; make BH = AB : draw any

straight line CED , cutting BC , BE , BD , in C , E , D . Join A C , A E , A D ; I D , I E ,

I C .

To prove this

**proposition**, it must be shown that A B is to any straight line BE ,drawn from B , in the plane mn . Produce AB to ; make BH = AB : draw any

straight line CED , cutting BC , BE , BD , in C , E , D . Join A C , A E , A D ; I D , I E ,

I C .

Página 8

others that meet one another , and are not in the same plane wilh the former two ,

the former two and the other two shall contain equal angles . Let A B , BC , which

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**PROPOSITION**X . If two straight lines meeting one another be parallel to twoothers that meet one another , and are not in the same plane wilh the former two ,

the former two and the other two shall contain equal angles . Let A B , BC , which

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Página 9

plane . מן | ת Let a be the given point in the plane : take any point B above the

plane , from which draw BC + to the plane : and then from a draw AD parallel to

CB ...

**PROPOSITION**XII . From a given point in a plane to draw a perpendicular to theplane . מן | ת Let a be the given point in the plane : take any point B above the

plane , from which draw BC + to the plane : and then from a draw AD parallel to

CB ...

Página 14

plane , their common section shall be perpendicular to the same plane . Let the

two planes AB , BC , be each 1 to the third plane , and let bo be the common ...

**PROPOSITION**XX . If two planes which intersect be each perpendicular to a thirdplane , their common section shall be perpendicular to the same plane . Let the

two planes AB , BC , be each 1 to the third plane , and let bo be the common ...

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### Palavras e frases frequentes

angle arcs assumed axes axis base called centre circle coincide common cone conic consequently considered construction contains corresponding curve curve of intersection cylinder described Descriptive determined developed dicular distance draw draw the tangent drawn equal evident example faces figure formed generatrixes given line given point ground line helix Hence horizontal plane horizontal projection horizontal trace intersection length line joining lines parallel magnitude meet moving necessary normals obtained obviously Octavo parallel parallel to xy perpen perpendicular plane pap plane passing planes of projection point of contact polygon position PROBLEM produced PROPOSITION radius required plane respectively right angles sides situated solid sought space sphere straight line supposed surface tangent plane third plane tion true vertex vertical plane vertical projection vertical trace

### Passagens conhecidas

Página 15 - A MANUAL of CHRISTIAN ANTIQUITIES ; or an Account of the Constitution, Ministers, "Worship, Discipline, and Customs of the Early Church ; with an Introduction, containing a Complete and Chronological Analysis of the "Works of the Antenicene Fathers.

Página 11 - If two straight lines meeting one another be parallel to two other straight lines which meet one another, but are not in the same plane with the first two; the plane which passes through these is parallel to the plane passing through the others.

Página 10 - From the same point in a given plane there cannot be two straight lines at right angles to the plane, upon the same side of it : and there can be but one perpendicular to a plane from a point above the plane.

Página 15 - HISTORY of the CHURCH of ENGLAND, to the REVOLUTION in 1688; embracing Copious Histories of the Thirty-Nine Articles, the Translation of the Bible, and the Compilation of the Book of Common Prayer.

Página 6 - IF two straight lines be parallel, the straight line drawn from any point in the one to any point in the other is in the same plane with the parallels.* Let AB, CD be parallel straight lines, and take any point E in the one, and the point F in the other : the straight line which joins E and F is in the same plane with the parallels.

Página 17 - BIBLE CYCLOPEDIA; a Comprehensive Digest of the Civil and Natural History, Geography, Statistics, and General Literary Information connected with the Sacred Writings.

Página 15 - CV. *HISTORY OF THE CHRISTIAN CHURCH ; from the Ascension of Jesus Christ to the Conversion of Constantine. By the late EDWARD BURTON, DD, Regius Professor of Divinity at Oxford.

Página 2 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.

Página 19 - Progressive Exercises in Greek Tragic Senarii, followed by a Selection from the Greek Verses of Shrewsbury School, and prefaced by a short Account of the Iambic Metre and Style of Greek Tragedy.

Página 7 - Two straight lines which are each of them parallel to the same straight line, and not in the same plane with it, are parallel to one another. Let AB...