Euclid's Elements of Geometry: From the Latin Translation of Commandine. To which is Added, a Treatise of the Nature and Arithmetic of Logarithms; Likewise Another of the Elements of Plane and Spherical Trigonometry; with a Preface, Shewing the Usefulness and Excellency of this WorkW. Strahan, 1772 - 399 Seiten |
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Seite xix
... greater Angle of every Triangle fubtends the greater Side .. LE ET ABC be a Triangle , having the Angle A B C greater than the Angle BCA . I fay , the Side A C is greater than the Side A B. * * For , if it be not greater , AC is either ...
... greater Angle of every Triangle fubtends the greater Side .. LE ET ABC be a Triangle , having the Angle A B C greater than the Angle BCA . I fay , the Side A C is greater than the Side A B. * * For , if it be not greater , AC is either ...
Seite xx
... greater Angle fubtends + the greater Side ; the Side DB will be greater than the Side BC . But DB is equal to B A and AC together . Wherefore the Sides BA , AC , together , are greater than the Side B C. In the fame manner we ...
... greater Angle fubtends + the greater Side ; the Side DB will be greater than the Side BC . But DB is equal to B A and AC together . Wherefore the Sides BA , AC , together , are greater than the Side B C. In the fame manner we ...
Seite xxi
... greater than the Angle CED . Wherefore the Angle BDC fhall be much greater than the Angle BAC . And fo , if two Right Lines be drawn from the extreme Points of one Side of a Triangle to any Point within the fame , thefe two Lines fhall ...
... greater than the Angle CED . Wherefore the Angle BDC fhall be much greater than the Angle BAC . And fo , if two Right Lines be drawn from the extreme Points of one Side of a Triangle to any Point within the fame , thefe two Lines fhall ...
Seite xxii
... greater than the Bafe of the other . ET there be two Triangles A B C , DEF , hav- ing two Sides A B , A C , equal to ... greater than the Angle EDF . fay , the Bafe BC is greater than the Bafe E E. For 23 of thin . For because the Angle ...
... greater than the Bafe of the other . ET there be two Triangles A B C , DEF , hav- ing two Sides A B , A C , equal to ... greater than the Angle EDF . fay , the Bafe BC is greater than the Bafe E E. For 23 of thin . For because the Angle ...
Seite xxiii
... greater than the Angle EDF ; make an Angle E DG at the Point Din the Right Line D E , equal to the Angle B AC ; and ... greater than the Angle E GF : And confe- quently the Angle EFG is much greater than the Angle EGF . And because EFG ...
... greater than the Angle EDF ; make an Angle E DG at the Point Din the Right Line D E , equal to the Angle B AC ; and ... greater than the Angle E GF : And confe- quently the Angle EFG is much greater than the Angle EGF . And because EFG ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2018 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2017 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
A B C adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle ABCD Circumference Cofine Cone confequently Coroll Cylinder defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fecond fhall be equal fimilar fince firft folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Reafon Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment ſhall Sides A B Sine Square Subtangent thefe THEOREM thofe thoſe tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe whoſe
Beliebte Passagen
Seite 195 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 165 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Seite 169 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Seite xxii - ... sides equal to them of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB...
Seite 54 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 123 - GB is equal to E, and HD to F; GB and HD together are equal to E and F together : wherefore as many magnitudes as...
Seite 215 - CD; therefore AC is a parallelogram. In like manner, it may be proved that each of the figures CE, FG, GB, BF, AE, is a parallelogram...
Seite 196 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.
Seite 161 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Seite 207 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. V. The inclination of a straight line to a plane...