The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page vii
... greater than Peloponnefus ( a notable Inftance of the Infancy of Aftro- nomy at that Time ) ; and that he made fome Conjectures concerning Habitations in the Moon . As for Oenopides , to him Proclus afcribes the 12 and 23. l . 1 . Thefe ...
... greater than Peloponnefus ( a notable Inftance of the Infancy of Aftro- nomy at that Time ) ; and that he made fome Conjectures concerning Habitations in the Moon . As for Oenopides , to him Proclus afcribes the 12 and 23. l . 1 . Thefe ...
Page 3
... Greater , whofe Side falls without . So the Angle B AE is greater than the Angle BAC . An Angle is not diminifh'd or increas'd by the Dimi- nution or Augmentation of the Sides that include it . Fig . s 13. A right - lin❜d Angle is that ...
... Greater , whofe Side falls without . So the Angle B AE is greater than the Angle BAC . An Angle is not diminifh'd or increas'd by the Dimi- nution or Augmentation of the Sides that include it . Fig . s 13. A right - lin❜d Angle is that ...
Page 8
... greater of them GH to cut off GI equal to the lefs EF . Take with a Pair of Compaffes the Interval of the leffer given Line EF , and transfer it unto the greater from G to I. Ive PROP . IV . Theorem . F in two Triangles ( X , Z ) one ...
... greater of them GH to cut off GI equal to the lefs EF . Take with a Pair of Compaffes the Interval of the leffer given Line EF , and transfer it unto the greater from G to I. Ive PROP . IV . Theorem . F in two Triangles ( X , Z ) one ...
Page 16
... greater Side ( BO ) is the greater ; and that ( B ) which is oppofite to the leffer Side ( A O ) is the leffer Angle . ( A ) Cannot be equal to ( B ) for then the oppofite ( 2 ) Per 6.1.1 . Sides BO , AO would be equal ( a ) ; which is ...
... greater Side ( BO ) is the greater ; and that ( B ) which is oppofite to the leffer Side ( A O ) is the leffer Angle . ( A ) Cannot be equal to ( B ) for then the oppofite ( 2 ) Per 6.1.1 . Sides BO , AO would be equal ( a ) ; which is ...
Page 17
... greater . 2. E. D. PROP . XIX . Theorem . 17 IN the and N the Triangle AO B the Side ( BO ) which is op- Fig . 38 . that ( AO ) which is oppofed to the leffer Angle B , is the leffer . This Propofition is the Converfe of the former . BO ...
... greater . 2. E. D. PROP . XIX . Theorem . 17 IN the and N the Triangle AO B the Side ( BO ) which is op- Fig . 38 . that ( AO ) which is oppofed to the leffer Angle B , is the leffer . This Propofition is the Converfe of the former . BO ...
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The Elements of Euclid: With Select Theorems Out of Archimedes Archimedes,André Tacquet,Euclid No preview available - 2015 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page xviii - Difcovery of Divine Truth : And of the Degree of Evidence that , ought to be expected in Divine Matters, 8vo.
Page 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.
Page 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.
Page 11 - Because the angle A is equal to the angle C, and the angle...
Page xviii - Bodies contained in the fame Syftem. VI.' Important Principles of NATURAL RELIGION Demonftrated from the foregoing Obfervations.
Page 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.
Page 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...
Page 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...