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 240
... Circles are to each other as the Squares of their Diameters . LETABCD. ,. EFGH. ,. be. Cireles. ,. whose. Dia-. meters are BD , FH . I fay , as the Square of BD is to the Square of FH , so the Circle ABCD is to the Circle EFGH . For , • For ...
... Circles are to each other as the Squares of their Diameters . LETABCD. ,. EFGH. ,. be. Cireles. ,. whose. Dia-. meters are BD , FH . I fay , as the Square of BD is to the Square of FH , so the Circle ABCD is to the Circle EFGH . For , • For ...
Seite 241
... Circle EFGH . First , let it be to a Space S , less than the Circle E FGH ; and let the Square E F G H be described in the Circle . ▽ This Square E FGH will be greater than half the Circle EFGH ; because , if we draw Tangents to the ...
... Circle EFGH . First , let it be to a Space S , less than the Circle E FGH ; and let the Square E F G H be described in the Circle . ▽ This Square E FGH will be greater than half the Circle EFGH ; because , if we draw Tangents to the ...
Seite 242
... Circle ABCD , similar to the Polygon EKFLGMHN . Wherefore , as the 1 of this . Square of BD is to the Square of FH ... EFGH . After the fame manner we likewise demonftrate , that the Square of FH to the Square of BD , is not as the ...
... Circle ABCD , similar to the Polygon EKFLGMHN . Wherefore , as the 1 of this . Square of BD is to the Square of FH ... EFGH . After the fame manner we likewise demonftrate , that the Square of FH to the Square of BD , is not as the ...
Seite 259
... Circles ABCD , EFGH , Axes KL , MN , and Diameters of the Bases A C , EG . I fay , as the Circle ABCD is to the Circle EFGH , fo is the Cone A L to the Cone EN . For , if it be not so , it shall be , as the Circle ABCD is to the Circle EFGH ...
... Circles ABCD , EFGH , Axes KL , MN , and Diameters of the Bases A C , EG . I fay , as the Circle ABCD is to the Circle EFGH , fo is the Cone A L to the Cone EN . For , if it be not so , it shall be , as the Circle ABCD is to the Circle EFGH ...
Seite 260
... Circle ABCD is to the Circle EFGH ; it shall be , as the Circle ABCD is to the Circle EFGH , so is the Polygon DTAYBQCV to the Polygon HOEPFRGS . But as the Circle ABCD is to the Circle EFGH , so is the Cone AL to the Solid X ( by ...
... Circle ABCD is to the Circle EFGH ; it shall be , as the Circle ABCD is to the Circle EFGH , so is the Polygon DTAYBQCV to the Polygon HOEPFRGS . But as the Circle ABCD is to the Circle EFGH , so is the Cone AL to the Solid X ( by ...
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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 |
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alfo alſo equal Altitude Angle ABC Angle BAC Bafe becauſe biſected Centre Circle ABCD Circle EFGH Circumference Cofine Cone conſequently Coroll Cylinder demonftrated deſcribed Diameter Diſtance drawn thro equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fimilar fince firſt folid Parallelepipedon fore fubtending given Right Line greater join leſs likewiſe Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Priſm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure ſame ſay ſecond Segment Semicircle ſhall be equal Sides ſince Sine ſome Sphere Square ſtand Subtangent THEOREM thereof theſe thoſe three Right Lines tiple Triangle ABC Unity Vertex the Point Wherefore whole whoſe Baſe
Beliebte Passagen
Seite 193 - 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 163 - 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 168 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Seite 18 - ... 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 52 - 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 121 - 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 213 - 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 194 - 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 159 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Seite 205 - 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...