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 ...T. Woodward, 1723 - 364 σελίδες |
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Σελίδα 2
... Angles on either Side thereof , equal between themfelves , each of these equal Angles is a Right one ; and that Right Line which ftands upon the other , is called a Perpendicular to that whereon it stands . XI . An Obtufe Angle , is ...
... Angles on either Side thereof , equal between themfelves , each of these equal Angles is a Right one ; and that Right Line which ftands upon the other , is called a Perpendicular to that whereon it stands . XI . An Obtufe Angle , is ...
Σελίδα 7
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle equal to the Angle contained by the correfpondent Sides in the other Triangle , then the Bafe of one of the Tri- angles fhall be ...
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle equal to the Angle contained by the correfpondent Sides in the other Triangle , then the Bafe of one of the Tri- angles fhall be ...
Σελίδα 8
... equal thereto ; and the remaining Angles + 4x . 8. will co - incide with the remaining Angles † , and will be equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle ACB equal to the An- gle DFE . Which was to be ...
... equal thereto ; and the remaining Angles + 4x . 8. will co - incide with the remaining Angles † , and will be equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle ACB equal to the An- gle DFE . Which was to be ...
Σελίδα 9
... equal Sides . And fo the Angle FBC is equal to the Angle GCB ; and the Angle BCF equal to the Angle CBG . Therefore ... Angles at the Bafe of the Triangle ABC . It hath likewife been proved that the Angles FBC , GC B , under the Bafe ...
... equal Sides . And fo the Angle FBC is equal to the Angle GCB ; and the Angle BCF equal to the Angle CBG . Therefore ... Angles at the Bafe of the Triangle ABC . It hath likewife been proved that the Angles FBC , GC B , under the Bafe ...
Σελίδα 14
... equal to HE , and HC is com- mon , GH and HC are each equal to EH and HC , and the Base CG is equal to the Bafe CE . Therefore Def . 10. the Angle CHG is equal to the Angle CHE ; and they are adjacent Angles . But when a Right Line ...
... equal to HE , and HC is com- mon , GH and HC are each equal to EH and HC , and the Base CG is equal to the Bafe CE . Therefore Def . 10. the Angle CHG is equal to the Angle CHE ; and they are adjacent Angles . But when a Right Line ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Σελίδα 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...
Σελίδα 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.
Σελίδα 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.