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 sider |
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Resultat 1-5 av 14
Side 64
... Similar Segments of Circles are those which include equal Angles , or whereof the Angles in them are equal . * 10. 1 . † II . I. PROPOSITION 1 . PROBLEM . To find the Center of a Circle given . ET ABC be the Circle given . It is re ...
... Similar Segments of Circles are those which include equal Angles , or whereof the Angles in them are equal . * 10. 1 . † II . I. PROPOSITION 1 . PROBLEM . To find the Center of a Circle given . ET ABC be the Circle given . It is re ...
Side 85
... Similar Segments of Circles being upon equal Right Lines , are equal to one another . LET AEB , CFD be equal Segments of Circles , standing upon the equal Right Lines AB , CD , I fay , the Segment A E B is equal to the Segment CFD . For ...
... Similar Segments of Circles being upon equal Right Lines , are equal to one another . LET AEB , CFD be equal Segments of Circles , standing upon the equal Right Lines AB , CD , I fay , the Segment A E B is equal to the Segment CFD . For ...
Side 167
... Similar Triangles are in the duplicate Proportion of their homologous Sides . LET ABC , DEF , be fimilar Triangles , having the Angle B equal to the Angle E ; and let A B be to BC as DE is to EF , fo that BC be the Side homologous to EF ...
... Similar Triangles are in the duplicate Proportion of their homologous Sides . LET ABC , DEF , be fimilar Triangles , having the Angle B equal to the Angle E ; and let A B be to BC as DE is to EF , fo that BC be the Side homologous to EF ...
Side 168
... Similar Polygons are divided into fimilar Triangles , e- qual in Number , and homologous to the Wholes ; and Polygon to Polygon , is in the duplicate Proportion of that which one homologous Side has to the other . LFT ABCDE , FGHKL , be ...
... Similar Polygons are divided into fimilar Triangles , e- qual in Number , and homologous to the Wholes ; and Polygon to Polygon , is in the duplicate Proportion of that which one homologous Side has to the other . LFT ABCDE , FGHKL , be ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Side 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...
Side 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.
Side 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Side 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...
Side 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.
Side 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.
Side 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.