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 Plain and Spherical Trigonometry : with a Preface ... |
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... Manner , would have us believe they have detected a great many Faults in Euclid . Thefe acute Philofophers , pretend to have difcover'd that Euclid's Definitions are not perfpicuous enough ; that his Demonftra . tions are fcarcely ...
... Manner , would have us believe they have detected a great many Faults in Euclid . Thefe acute Philofophers , pretend to have difcover'd that Euclid's Definitions are not perfpicuous enough ; that his Demonftra . tions are fcarcely ...
Page 15
... Manner it is demonftrated , that no other Line but BD is in a ftraight Line with CB ; wherefore CB , BD , fhall be in one ftraight Line . Therefore if to any Right Line , and Point therein two Right Lines be drawn from contrary Parts ...
... Manner it is demonftrated , that no other Line but BD is in a ftraight Line with CB ; wherefore CB , BD , fhall be in one ftraight Line . Therefore if to any Right Line , and Point therein two Right Lines be drawn from contrary Parts ...
Page 17
... manner , if the Right Line BC , be bifected , we demonftrate that the Angle BCG , that is , the Angle ACD , is greater than the Angle ABC . Therefore one Side of any Triangle being produced , the outward Angle is greater than either of ...
... manner , if the Right Line BC , be bifected , we demonftrate that the Angle BCG , that is , the Angle ACD , is greater than the Angle ABC . Therefore one Side of any Triangle being produced , the outward Angle is greater than either of ...
Page 18
... manner we demonftrate that the Angles . BAC , ACB , as alfo CAB , ABC , are lefs than two Right Angles . Therefore two Angles of any Tri- angle together , howsoever taken , are less than two Right Angles ; which was to be demonstrated ...
... manner we demonftrate that the Angles . BAC , ACB , as alfo CAB , ABC , are lefs than two Right Angles . Therefore two Angles of any Tri- angle together , howsoever taken , are less than two Right Angles ; which was to be demonstrated ...
Page 18
... manner we demonftrate that the Angles BAC , ACB , as alfo CAB , ABC , are lefs than two Right Angles . Therefore two Angles of any Tri- angle together , howsoever taken , are less than two Right Angles ; which was to be demonstrated ...
... manner we demonftrate that the Angles BAC , ACB , as alfo CAB , ABC , are lefs than two Right Angles . Therefore two Angles of any Tri- angle together , howsoever taken , are less than two Right Angles ; which was to be demonstrated ...
Common terms and phrases
alfo equal alſo Angle ABC Angle BAC Baſe becauſe bifected Center Circle ABCD Circle EFGH Circumference Cofine Cone confequently contain'd Coroll Cylinder defcrib'd defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number paffing thro Parallelogram perpendicular Polygon Prifm Priſms Prop PROPOSITION Pyramid Quadrant Ratio Rectangle remaining Angle Right Angles Right Line A B Right Line AB Right-lin'd Figure Right-lin❜d Segment ſhall Sine Solid Sphere Subtangent thefe THEOREM theſe thofe Triangle ABC triplicate Proportion Unity Vertex the Point Wherefore whofe Bafe whole
Popular passages
Page 190 - 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.
Page 160 - 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.
Page 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Page 152 - ... therefore the angle DFG is equal to the angle DFE, and the angle at G to the angle at E : but the angle DFG is equal to the angle ACB...
Page 100 - About a given circle to describe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to describe a triangle about the circle ABC equiangular to the triangle DEF.
Page 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Page 210 - 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...
Page 229 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Page 164 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Page 93 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.