Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To which is Added, A Treatise of the Nature of Arithmetic of Logarithms; Likewise Another of the Elements of Plain and Spherical Trigonometry; with a Preface...Tho. Woodward at the Half-Moon, between the Two Temple-Gates in Fleet-street; and sold by, 1733 - 397 Seiten |
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Seite 64
... Similar Segments of Circles are thofe which include equal Angles , or whereof the Angles in them are equal . PROPOSITION I. PROBLEM . To find the Center of a Circle given . L ET ABC be the Circle given . It is re- quired to find the ...
... Similar Segments of Circles are thofe which include equal Angles , or whereof the Angles in them are equal . PROPOSITION I. PROBLEM . To find the Center of a Circle given . L ET ABC be the Circle given . It is re- quired to find the ...
Seite 85
... Similar Segments of Circles being upon equal Right Lines , are equal to one another . ET AEB , CFD be equal Segments of Circles ftanding upon the equal Right Lines AB , CD . I fay , the Segment AEB is equal to the Segment CFD . For the ...
... Similar Segments of Circles being upon equal Right Lines , are equal to one another . ET AEB , CFD be equal Segments of Circles ftanding upon the equal Right Lines AB , CD . I fay , the Segment AEB is equal to the Segment CFD . For the ...
Seite 158
... similar to one another , and to the whole Triangle ABC . For because the Angle BAC is equal to the Angle ADB , for each of them is a Right Angle , and the Angle at B is common to the two Triangles A BC , Cor . 32. 1. ABD , the remaining ...
... similar to one another , and to the whole Triangle ABC . For because the Angle BAC is equal to the Angle ADB , for each of them is a Right Angle , and the Angle at B is common to the two Triangles A BC , Cor . 32. 1. ABD , the remaining ...
Seite 167
... Similar Triangles are in the duplicate Proportion of their homologous Sides . ET ABC , DEF , be fimilar Triangles , having the Angle B equal to the Angle E ; and let AB 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 . ET ABC , DEF , be fimilar Triangles , having the Angle B equal to the Angle E ; and let AB be to BC as DE is to EF , fo that BC be the Side homologous to EF ...
Seite 168
... Similar Polygons are divided into fimilar Triangles , equal in Number , and homologous to the Wholes ; and Polygon to Polygon , is in the duplicate Pro- portion of that which one homologous Side has to the other . ET ABCDE , F GHKL , be ...
... Similar Polygons are divided into fimilar Triangles , equal in Number , and homologous to the Wholes ; and Polygon to Polygon , is in the duplicate Pro- portion of that which one homologous Side has to the other . ET ABCDE , F GHKL , be ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
adjacent Angles alfo equal alſo Angle ABC Angle BAC Bafe Baſe becauſe bifected Center Circle ABCD Circumference Cofine Cone confequently Coroll Cylinder defcribed demonftrated Diameter Diſtance drawn thro EFGH equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs leſs likewife Logarithm Magnitudes Meaſure Number Parallelogram perpendicular Polygon Priſms Prop PROPOSITION Pyramid Pyramid ABCG Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line AC Right-lined Figure Segment ſhall Sine Solid Sphere Subtangent themſelves THEOREM theſe thofe thoſe Triangle ABC Unity Vertex the Point Wherefore whofe Bafe whole whoſe Baſe
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Seite 66 - 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 112 - And in like manner it may be shown that each of the angles KHG, HGM, GML is equal to the angle HKL or KLM ; therefore the five angles GHK, HKL, KLM, LMG, MGH...
Seite 90 - IN a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 22 - ... 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 10 - ... 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 equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Seite 15 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Seite 33 - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other, (i.
Seite 113 - 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.