Imagens das páginas
PDF
ePub

m, found as before, and then m, must be transferred to its true position by taking the point n in the same position as regards ob, that m has to ob. Which is done by describing a circle from a as a centre with om, for a radius, and making the arc en equal to dm, of that circle.

2°. Construction of the Tangent. The epicycloid, as has been already observed, lies on the surface of a sphere, having 0,0' for its centre, and oʻb for its radius, consequently the tangent to the point m, m' of this curve is in the tangent plane to this sphere. It has also been proved to lie in the tangent plane to a sphere, the centre of which would be in b, and the radius of which would be bm; the intersection of these two tangent planes must therefore be the tangent in question.

The base of the moving cone, which is turned down in the circle bmc, belongs to the first of these spheres; if therefore a tangent mf is drawn to the circle bmc at the point m, it will be a line situated in the tangent plane to the sphere turned down with bmc on the horizontal plane, consequently the point f, in which mf meets bc, is in the horizontal trace of this plane. This trace must therefore be the line d'f drawn from f, perpendicular to the projection om of the line, which passes through the point of contact.

The circle described with the radius bm is one of the second sphere, also turned down on the horizontal plane, if Mg be drawn a tangent to it, meeting bc in g, and be drawn perpendicular to bm, the line will be the horizontal trace of the tangent plane to the second sphere. The traces d'f, Bg meet in r, which must belong to the intersection of the two tangent planes, the line mr, drawn through this point r and through m, must consequently be the projection of the tangent to the epicycloid, or, which is the same thing, a tangent to the projection of that curve.

LONDON:-HARRISON AND Co., PRINTERS, St. Martin's Lane.

PUBLISHED BY

JOHN W. PARKER, WEST STRAND,

LONDON,

MANUAL OF CHRISTIAN ANTIQUITIES; Or, An Account of the Constitution, Ministers, Worship, Discipline, and Customs of the Early Church : with a Complete Analysis

of the Works of the Antenicene Fathers.
By the Rev. J. E. RIDDLE, M.A. Octavo, 18s.

THE CIVIL HISTORY OF THE JEWS, From Joshua to Adrian ; with Notices of Manners and Customs, Geo. graphy and Antiquities. By the Rev. 0. COCKAYNE, M.A.,

King's College, London. 48. 6d.

THE CHURCHMAN'S GUIDE; A Copious Index of Sermons and other Works, by eminent Church of England Divines; digested and arranged according to their

subjects, and continued to the present day. By the Rev. JOHN FORSTER, M.A., Incumbent of the Royal Chapel

in the Savoy. Octavo, 78.

HISTORY OF THE CHRISTIAN CHURCH, From the Ascension of Jesus Christ to the Conversion of Constantine

By the late EDWARD BURTON, D.D. Fourth Edition, 6s. 6d.

HISTORY OF THE CHURCH OF ENGLAND, To the Revolution in 1688; embracing Copious Histories of the ThirtyNine Articles, the Translation of the Bible, and the Compila

tion of the Book of Common Prayer. By the Right Rev. Thomas VoWLER SHORT, D.D., Lord Bishop of

Sodor and Man, Third Edition. 16s.

HISTORY OF THE CHURCH of IRELAND;
By the Right Rev. RICHARD Mant, D.D., Lord Bishop of Down and

Connor. Two large Volumes, Octavo, 178. each.
VOL. I.-From the Reformation to the Revolution.
VOL. II.-From the Revolution to the Union.

LECTURES IN DIVINITY, Delivered in the University of Cambridge, by John Hey, D.D., as Norrissian Professor, from 1780 to 1795. A New Edition,

Revised, in Two Large Volumes, 30s.

ECCLESIÆ ANGLICANÆ VINDEX CATHOLICUS Sive Articulorum Ecclesiæ Anglicanæ cum Scriptis SS. Patrum nova collatio cura GULIELMI W. HARVEY, A.M., Collegii

Regalis Socii. Tom. I. 18s.

THE BOOK OF THE FATHERS OF THE CHRIS

TIAN CHURCH,
And the Spirit of their Writings. Octavo, 9s. 6d.

ELIZABETHAN RELIGIOUS HISTORY.

By the Rev. HENRY SOAMES, M.A. Octavo, 16s.

A HISTORY OF POPERY, And of its Influence on Society. With Accounts of the Inquisition, and State of Popery in Ireland, and Specimens of Romish

Legends. Octavo, 9s. 6d.

LUTHER AND HIS TIMES; Or, History of the Rise and Progress of the German Reformation.

By the Rev. J. E. RIDDLE, M.A. 58.

THE LIFE OF ARCHBISHOP SANCROFT. By GEORGE D'Oyly, D.D., F.R.S., Rector of Lambeth. Octavo,

Second Edition, Revised, with a Portrait. 98.

MEMOIRS OF THE LIFE, CHARACTER, AND
WRITINGS OF BISHOP BUTLER,

Author of The Analogy.
By THOMAS BARTLETT, M.A., Rector of Kingstone, Kent.

Octavo, 128., with an original Portrait.

THE HANDMAID; Or, the Pursuits of Literature and Philosophy, considered as subservient

to the Interests of Morality and Religion. By the Rev. John Davies, B.D., Author of an Estimate of the

Human Mind. 48.

BIBLE CYCLOPÆDIA. A Comprehensive Digest of the Civil and Natural History, Geography, Statistics, and General Literary Information connected with the

Sacred Writings. Small Folio, to be completed in about Thirty Monthly Numbers, price ls. 6d. each ; forming Two handsome volumes, illustrated by several hundred woodcuts. The First Volume, price 258., and the Sixteen Numbers, are already published.

BIBLE MAPS;
With Explanatory Memoirs, and a Copious Index of Scriptural and
Modern Names, and forming a complete Historical and Descriptive

Atlas of Scripture Geography.
Uniform with the BIBLE CYCLOPÆDIA.
By WILLIAM HUGHES, F.R.G.S. 78. 6d.

SACRED MINSTRELSY;
A COLLECTION OF THE FINEST SACRED MUSIC,
By the best Masters, arranged as Solos, Duets, Trios, &c., and with

Accompaniments for the Piano-Forte or Organ.
Two Handsome Folio Volumes, price £2. 2s. half-bound.

ORIGINAL FAMILY SERMONS;
By ONE HUNDRED and FIFTY CONTEMPORARY DIVINES of the

ESTABLISHED CHURCH.
Five Volumes at 6s. 6d. each.

Dedicated by Special Permission to Her Majesty.
THE EVIDENCE OF PROFANE HISTORY TO THE

TRUTH OF REVELATION.
Post Octavo, with Numerous Illustrations. 108. 6d.

THE EARLY CHRISTIANS;
THEIR MANNERS AND CUSTOMS, TRIALS AND SUFFERINGS.

By the Rev. W. PRIVDEN, M.A. Third Edition. 4s.

LIVES OF EMINENT CHRISTIANS. By R. B. HONE, M.A., Vicar of Hales Owen Foolscap Octavo,

Three Volumes, at 4s. 6d. each.

LIVES OF ENGLISH SACRED POETS: With an INTRU JUCTORY SKETCH of EARLY SACRED POETRY aná Poets.

By R. A. WILLMOTT, B.A., Trinity College, Cambridge.

Two Volumes, with Portraits, price 4s. 6d. each.

THE SCRIPTURAL CHARACTER OF THE

ENGLISH CHURCH CONSIDERED, In a Series of Sermons, with copious Notes and Illustrations.

By the Rev. DERWENT COLERIDGE, M.A. Octavo, 128. 6d.

GARRICK'S INSTRUCTIONS FOR READING

THE LITURGY,
With Notes, and a Discourse on Public Reading.
By RICHARD CULL, Tutor in Elocution. Octavo, 58. 6d.

THE RITUAL OF THE UNITED CHURCH OF ENG.

LAND AND IRELAND ILLUSTRATED. With occasional Reference to the Objections of Dissenters. By the Rev. G. W. TYRREL, A.M., Secretary of the Down and Connor

Diocesan Church Education Society. 6s.

THE BOOK OF COMMON PRAYER

ILLUSTRATED, So as to show its various Modifications, the Date of its several Parts,

and the Authority on which they rest. With an Appendix. By WILLIAM KRATING CLAY, B.D., Minor Canon of Ely. 7s. 6d. EXPLANATORY NOTES ON THE PRAYER-BOOK

VERSION OF THE BOOK OF PSALMS,
With Copious Marginal References. By the Same. 78. 6d.

ON THE FOUNDATIONS OF MORALS:
Four Sermons Preached before the University of Cambridge. By the
Rev. PROFESSOR WHEWELL, F.R.S., Master of Trinity College.

Second Edition, with a Preface. 38. 6d.

THE WORKS OF DOCTOR DONNE;

With a Memoir of his Life,
By HENRY ALFORD, M. A., Vicar of Wymeswould.

Six Volumes, Octavo, with Portrait. 31. 128.

THE GREEK TEXT OF THE ACTS OF THE

APOSTLES; With Notes, Original and Selected ; for the use of Students in the

University. By HASTINGS ROBINSON, D.D., F.A.S. 88.

« AnteriorContinuar »