The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page xiii
... Spherical Triangles . Three most useful Books of Sphericks of Theodofi us the Tripolite are alfo in the Hands of all . And these indeed , if you except Me- nelaus , lived all of them before Christ . + 70 , there ap- In the Year after ...
... Spherical Triangles . Three most useful Books of Sphericks of Theodofi us the Tripolite are alfo in the Hands of all . And these indeed , if you except Me- nelaus , lived all of them before Christ . + 70 , there ap- In the Year after ...
Page 17
... spherical Surface . I PRO P. XX . Theorem . N any Triangle , any two Sides of it taken together , are greater than the remaining Side . This with Archimedes is as it were an Axiom ; for- afmuch as it is immediately manifeft out of his ...
... spherical Surface . I PRO P. XX . Theorem . N any Triangle , any two Sides of it taken together , are greater than the remaining Side . This with Archimedes is as it were an Axiom ; for- afmuch as it is immediately manifeft out of his ...
Page 59
... Sphere only in one Point . I PROP . III . Theorem . Fin a Circle a right Line ( BL ) drawn thro ' the Fig . 3 Centre bifects another ( CF ) not drawn thro ' the Cen TM tre , it will cut it perpendicularly . And if it cut it per ...
... Sphere only in one Point . I PROP . III . Theorem . Fin a Circle a right Line ( BL ) drawn thro ' the Fig . 3 Centre bifects another ( CF ) not drawn thro ' the Cen TM tre , it will cut it perpendicularly . And if it cut it per ...
Page 62
... Sphere , from any Point diverfe from the Pole of a certain Circle , unto that Circle , the greatest is that which paffeth thro ' the Pole of that Circle ; the least , that which is drawn unto the oppofite Point ; and of the reft , that ...
... Sphere , from any Point diverfe from the Pole of a certain Circle , unto that Circle , the greatest is that which paffeth thro ' the Pole of that Circle ; the least , that which is drawn unto the oppofite Point ; and of the reft , that ...
Page 82
... Sphere . Tea , if a Veffel be elevated conti- nually higher and higher , the Surface of the Water which is contain'd in it , will continually defcend and come nearer unto a Plane ; unto which yet it will ne- ver actually come . ( 5 ...
... Sphere . Tea , if a Veffel be elevated conti- nually higher and higher , the Surface of the Water which is contain'd in it , will continually defcend and come nearer unto a Plane ; unto which yet it will ne- ver actually come . ( 5 ...
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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...