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 8
... fame Plane , as the first fix Elements were , claimed by a Right of Order , to be handled before Planes interfected by Planes , or the more ... two ; one of which was a fecond Demonftration of the 9th Propo- fition of the third Book ; and the ...
... fame Plane , as the first fix Elements were , claimed by a Right of Order , to be handled before Planes interfected by Planes , or the more ... two ; one of which was a fecond Demonftration of the 9th Propo- fition of the third Book ; and the ...
Seite 10
... fame Time the Sides BA , AC , fhould not co - incide with the Sides ED , DF , but change their Position , as EG , GF , then there would be conftituted on the fame Right Line two Right Lines , equal to two other Right Lines , each to ...
... fame Time the Sides BA , AC , fhould not co - incide with the Sides ED , DF , but change their Position , as EG , GF , then there would be conftituted on the fame Right Line two Right Lines , equal to two other Right Lines , each to ...
Seite 32
... twice as many Right Angles as the Fi- gure has Sides ; but from the last Theorem , all the inward Angles together make ... fame Parts , are alfo equal and parallel . ET the parallel and equal Right Lines AB , CD , be joined towards the ...
... twice as many Right Angles as the Fi- gure has Sides ; but from the last Theorem , all the inward Angles together make ... fame Parts , are alfo equal and parallel . ET the parallel and equal Right Lines AB , CD , be joined towards the ...
Seite 69
... fame Line . And of all the other Lines , the nearest to that which was drawn thro ' the Center , is al- ways greater than that more remote , and only two equal Lines fall from the abovefaid Points upon the Circumference , on each Side ...
... fame Line . And of all the other Lines , the nearest to that which was drawn thro ' the Center , is al- ways greater than that more remote , and only two equal Lines fall from the abovefaid Points upon the Circumference , on each Side ...
Seite 70
... fame Line . And of all the other Lines , the nearest to that which was drawn through the Center , is always greater than that more remote ; and only two equal Lines fall from the abovefaid Point upon the Circum- ference , on each Side ...
... fame Line . And of all the other Lines , the nearest to that which was drawn through the Center , is always greater than that more remote ; and only two equal Lines fall from the abovefaid Point upon the Circum- ference , on each Side ...
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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.