The Elements of Euclid: With Select Theorems Out of Archimedes |
From inside the book
Results 1-5 of 17
Page xii
... Remains we have of Ar- chimedes , and many we have loft . and Archimedes . in Laftly , But when I name Archimedes , I conceive my Mind the very Top of humane Sub- tilty , and the Perfection of the whole Mathematical Sciences . His ...
... Remains we have of Ar- chimedes , and many we have loft . and Archimedes . in Laftly , But when I name Archimedes , I conceive my Mind the very Top of humane Sub- tilty , and the Perfection of the whole Mathematical Sciences . His ...
Page 15
... remains ( f ) LAB equal to CA F. In the fame manner ( † ) Per axi , 3 , BAF , LAC are fhewed to be equal . Coroll . From these two Propofitions we gather in Ca- toptricks , that a Ray of Light , as reflected in an Angle equal to the ...
... remains ( f ) LAB equal to CA F. In the fame manner ( † ) Per axi , 3 , BAF , LAC are fhewed to be equal . Coroll . From these two Propofitions we gather in Ca- toptricks , that a Ray of Light , as reflected in an Angle equal to the ...
Page 32
... remains but equal to the other , by the Force of the present Demon- Atration . [ From hence it follows , that two Cities in Magnitude equal , may fo much differ in Compass , that the Circum- ference of one may exceed that of the other ...
... remains but equal to the other , by the Force of the present Demon- Atration . [ From hence it follows , that two Cities in Magnitude equal , may fo much differ in Compass , that the Circum- ference of one may exceed that of the other ...
Page 56
... remains Rect . IAL equal to A Bq ; that is , Because AC and A L'are equal , the Rect . CI equal to A B Square , and confequently A B Square equal to ( d ) By the the Rectilinear ( d ) QX Z. Conftru & i- on . ( 1 ) P'er Coroll . Scholium ...
... remains Rect . IAL equal to A Bq ; that is , Because AC and A L'are equal , the Rect . CI equal to A B Square , and confequently A B Square equal to ( d ) By the the Rectilinear ( d ) QX Z. Conftru & i- on . ( 1 ) P'er Coroll . Scholium ...
Page 61
... remains greater than CF. fame . In the fame manner CF is prov'd to be less than CQ , or any other . Part 3. In the Triangles COA , CLA , the Sides L A , AC , are equal to OA , AC , each to each . But the Angle LAC is greater than the ...
... remains greater than CF. fame . In the fame manner CF is prov'd to be less than CQ , or any other . Part 3. In the Triangles COA , CLA , the Sides L A , AC , are equal to OA , AC , each to each . But the Angle LAC is greater than the ...
Other editions - View all
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...