The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page 62
... equal Arches can be drawn from that Point unto the Circle . And in the like manner may the Reader reason of himself on some other of the Propofitions of this Book ; it being very easy to pass from Planes to Solids in thefe ...
... equal Arches can be drawn from that Point unto the Circle . And in the like manner may the Reader reason of himself on some other of the Propofitions of this Book ; it being very easy to pass from Planes to Solids in thefe ...
Page 102
... Same , be ever changed and ordered in the very same manner . And then there will be no Room to question , whether the Proportions which arife on both Sides be alike or no . It is indeed a Thing to be wonder'd at , that no one of those ...
... Same , be ever changed and ordered in the very same manner . And then there will be no Room to question , whether the Proportions which arife on both Sides be alike or no . It is indeed a Thing to be wonder'd at , that no one of those ...
Page 178
... manner true of the Su- perficies . Fig . 23 , 24 . Cr PRO P. XIV . Theorem . Ylinders ( A R and CI ) of equal Bafes ( MQ , GB ) are as their Altitudes ( LZ , SF ) . The Same Thing happens to Cones . Cut off from the higher Cylinder AR ...
... manner true of the Su- perficies . Fig . 23 , 24 . Cr PRO P. XIV . Theorem . Ylinders ( A R and CI ) of equal Bafes ( MQ , GB ) are as their Altitudes ( LZ , SF ) . The Same Thing happens to Cones . Cut off from the higher Cylinder AR ...
Page
... Same Sphere . Let SK T and DOF be the equilateral Cones in- fcrib'd and circumfcrib'd , and let OKB be the com- mon ... manner , because the Side ST of the o- ther equilateral Triangle cuts off BC a 4th Part of the Axis BK , NO will be ...
... Same Sphere . Let SK T and DOF be the equilateral Cones in- fcrib'd and circumfcrib'd , and let OKB be the com- mon ... manner , because the Side ST of the o- ther equilateral Triangle cuts off BC a 4th Part of the Axis BK , NO will be ...
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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...