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 páginas |
Dentro del libro
Resultados 1-5 de 46
Página 16
... fame Reason , the Angle CEB fhall be equal to the Angle DEA . Therefore , if two Right Lines mutu- ally cut each other , the oppofite Angles are equal , which was to be demonftrated . † Ax . 3 . Coroll . 1. From hence it is manifeft ...
... fame Reason , the Angle CEB fhall be equal to the Angle DEA . Therefore , if two Right Lines mutu- ally cut each other , the oppofite Angles are equal , which was to be demonftrated . † Ax . 3 . Coroll . 1. From hence it is manifeft ...
Página xx
... fame manner we demonftrate , that the Sides AB , BC , together , are greater ... fame , these two Lines shall be less than the other two Sides of the Triangle ... Reason , CED , the outward Angle of the Triangle A BE , is likewife greater ...
... fame manner we demonftrate , that the Sides AB , BC , together , are greater ... fame , these two Lines shall be less than the other two Sides of the Triangle ... Reason , CED , the outward Angle of the Triangle A BE , is likewife greater ...
Página 36
... fame Parallels , are equal between themselves . LET ET the Parallelograms A BCD , EFGH , be conftituted upon the ... Reason , the Parallelogram EF G H is equal to the fame Parallelogram EBCH . Therefore the Pa- rallelogram ABCD fhall be ...
... fame Parallels , are equal between themselves . LET ET the Parallelograms A BCD , EFGH , be conftituted upon the ... Reason , the Parallelogram EF G H is equal to the fame Parallelogram EBCH . Therefore the Pa- rallelogram ABCD fhall be ...
Página 56
... fame Reasons are alfo C E B , E BC , each of them half a Right Angle . Therefore the whole Angle A E B is a Right Angle . And fince the Angle GEF is half a † 29. 1. Right one , and EGF is a Right Angle ; for it is + equal to the inward ...
... fame Reasons are alfo C E B , E BC , each of them half a Right Angle . Therefore the whole Angle A E B is a Right Angle . And fince the Angle GEF is half a † 29. 1. Right one , and EGF is a Right Angle ; for it is + equal to the inward ...
Página 84
... fame Reason , the Angle FEC is double to E AC . Therefore the whole Angle BEC is double to the whole Angle BAC . Again , let there be another Angle BDC ; and join DE , which produce to G. We demon- ftrate , in the fame manner , that the ...
... fame Reason , the Angle FEC is double to E AC . Therefore the whole Angle BEC is double to the whole Angle BAC . Again , let there be another Angle BDC ; and join DE , which produce to G. We demon- ftrate , in the fame manner , that the ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Sin vista previa disponible - 2018 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Sin vista previa disponible - 2017 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 169 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Página 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...
Página 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.
Página 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...
Página 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...
Página 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.
Página 161 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Página 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...