## The Elements of Descriptive Geometry ... |

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Página 50

There are curves called curves of double curvature , which are not in the same

plane : such is the

trace such a curve by the motion of a point , and thus say generally , that curves ...

There are curves called curves of double curvature , which are not in the same

plane : such is the

**helix**, of which the corkscrew is a familiar instance . We mighttrace such a curve by the motion of a point , and thus say generally , that curves ...

Página 94

This mode of generation shows that if the cylinder be developed on a plane , the

base becomes a right line , perpendicular to the generatrixes ; and the

consequently , develops into a straight line , oblique to these generatrixes .

This mode of generation shows that if the cylinder be developed on a plane , the

base becomes a right line , perpendicular to the generatrixes ; and the

**helix**,consequently , develops into a straight line , oblique to these generatrixes .

Página 95

tion of the

setting off the constant distance a ' a " along the projections of the generatrixes ,

from each point of the first , which is obviously equivalent to a repetition of the ...

tion of the

**helix**. And any number of consecutive revolutions may be drawn bysetting off the constant distance a ' a " along the projections of the generatrixes ,

from each point of the first , which is obviously equivalent to a repetition of the ...

Página 94

If , therefore , we develop the cylinder and the

cylindrical surface in the generatrix , passing through the point of contact , the

Another ...

If , therefore , we develop the cylinder and the

**helix**into a plane , touching thecylindrical surface in the generatrix , passing through the point of contact , the

**helix**when developed will coincide with the tangent to the curve at that point .Another ...

Página 95

tion of the

setting off the constant distance a ' a " along the projections of the generatrixes ,

from each point of the first , which is obviously equivalent to a repetition of the ...

tion of the

**helix**. And any number of consecutive revolutions may be drawn bysetting off the constant distance a ' a " along the projections of the generatrixes ,

from each point of the first , which is obviously equivalent to a repetition of the ...

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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...