The Elements of Euclid: With Select Theorems Out of ArchimedesJ. Senex ... W. and J. Innys ... and J. Osborn and T. Longman, 1727 - 239 Seiten |
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Seite 8
... shall now mea- fure the acceffible Line BC , you have the Measure of the inacceffible AB . QE . F. PRO P. II . Problem . Rom a given Point A to draw a right Line equal to one given EF , FR Take with a Pair of Compaffes the Interval E F ...
... shall now mea- fure the acceffible Line BC , you have the Measure of the inacceffible AB . QE . F. PRO P. II . Problem . Rom a given Point A to draw a right Line equal to one given EF , FR Take with a Pair of Compaffes the Interval E F ...
Seite 20
... shall have two Sides ( B A , AC ) equal to two ( B A , AF ) each to each ; and if one of the Triangles hath the Angle ( B AF ) contained by thofe Sides greater than the other ( BAC ) ; it fhall have the Bafe B F greater than the Bafe ...
... shall have two Sides ( B A , AC ) equal to two ( B A , AF ) each to each ; and if one of the Triangles hath the Angle ( B AF ) contained by thofe Sides greater than the other ( BAC ) ; it fhall have the Bafe B F greater than the Bafe ...
Seite 21
... Shall be equal to the inacceffible A D. 2. E. I. I PROP . XXVIL Theorem . F the right Line G Ofball cut two right Lines which Fig . 45 . are parallel ( A B , CF ) ; 1. The alternate Angles RLO , QO L , likewife B LO , COL ) fhall be ...
... Shall be equal to the inacceffible A D. 2. E. I. I PROP . XXVIL Theorem . F the right Line G Ofball cut two right Lines which Fig . 45 . are parallel ( A B , CF ) ; 1. The alternate Angles RLO , QO L , likewife B LO , COL ) fhall be ...
Seite 22
... shall be equal to two right ones , as likewife the two ( BLO , FOL ) equal to two right ones . A The firft Part is thus proved . the Perpendiculars O R , LQ . From O and L draw These are perpendicu- Per , Ax.11.lar to the two Parallels ...
... shall be equal to two right ones , as likewife the two ( BLO , FOL ) equal to two right ones . A The firft Part is thus proved . the Perpendiculars O R , LQ . From O and L draw These are perpendicu- Per , Ax.11.lar to the two Parallels ...
Seite 23
... shall make the two internal Angles on the fame Side ( ALO , CO L ) equal to two right Angles ; ( AB , CF ) are parallel Lines . By the 15th of this Book GL B is equal to ALO , which is vertically oppofite to it . But by the Hypothe- fis ...
... shall make the two internal Angles on the fame Side ( ALO , CO L ) equal to two right Angles ; ( AB , CF ) are parallel Lines . By the 15th of this Book GL B is equal to ALO , which is vertically oppofite to it . But by the Hypothe- fis ...
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The Elements of Euclid: With Select Theorems Out of Archimedes Archimedes,André Tacquet,Euclid Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
alfo alfo equal alſo Altitude Arch Archimedes Axis Bafe Baſe becauſe betwixt themſelves bifected Centre Circum circumfcrib'd Circumference confequently Conftruction conical Superficies conical Surfaces contain'd Coroll Corollary Cylinder defcrib'd defcribe demonftrated Diameter double drawn thro equal Angles equilateral Cone equilateral Triangle Euclid faid fame manner fcrib'd fecond felf fhall be equal fhew fhew'd Figure firft firſt folid Angle fome fore foregoing four right ftand fuppos'd given right Line greater hath Height Hypothefis infcrib'd infcribed Interfections leffer lefs likewife Line BC manifeft Mathematicks mean Proportional betwixt Meaſure Number oppofite pafs thro parallel Parallelepiped Parallelogram Pentagon perpendicular Plane Point Polygon Prifm Priſms Proclus produc'd PROP Propofition Pyramids Radius Rectangle right Angle right Line Scholium Segment Semidiameter Solid Sphere Square thefe Theorem theſe Thing thofe unto whatſoever whofe whole Superficies
Beliebte Passagen
Seite 21 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite xviii - A Scheme of the Solar Syftem, with the orbits of the planets and comets belonging thereto, defcribed from Dr. Halley's accurate Table of Comets, Philofoph.
Seite xviii - Difcovery of Divine Truth : And of the Degree of Evidence that , ought to be expected in Divine Matters, 8vo.
Seite xviii - Syllem briefly demonftrated. IV. Certain Obfervations drawn from that Syftem. V. Probable Conjectures of the Nature and Ufes of the feveral celeftial Bodies contain'd in the fame Syflem.
Seite xviii - DHcovery of divine Truth, and of the degree of Evidence that ought to be expected in divine Matters. By William WbiftvK, MA Ibmetime Profeffor of the Mathematicks in the Univerfity of Cambridge.
Seite 11 - Because the angle A is equal to the angle C, and the angle...
Seite xviii - Bodies contained in the fame Syftem. VI.' Important Principles of NATURAL RELIGION Demonftrated from the foregoing Obfervations.
Seite xix - How great a Geometrician art thou, O Lord! For while this Science has no Bounds, while there is for ever room for the Discovery of New Theorems, even by Human Faculties; Thou art acquainted with them all at one View, without any Chain of Consequences, without any Fatigue of Demonstrations.
Seite 211 - Side next to the Diameter : and let the right Lines BH, CG, DF, join the Angles which are equally diftant from A. I fay that the...
Seite 221 - Axis, is alfo given j it is manifeft that each of the Segments become known. Now both the foregoing, and all the reft of the Theorems which follow...