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 Plane and Spherical Trigonometry; with a Preface, Shewing the Usefulness and Excellency of this WorkW. Strahan, 1772 - 399 Seiten |
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Seite 11
... equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends which the first Right Lines have . FOR , if it be poffible , let two Right Lines AD , D B , equal to two others A C , CB ...
... equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends which the first Right Lines have . FOR , if it be poffible , let two Right Lines AD , D B , equal to two others A C , CB ...
Seite 11
... equal to two Sides of the other , each to each , and the Bafes equal , then the Angles contained under the equal Sides will be equal . LET the two Triangles be ABC , DEF , having two Sides , A B , AC , equal to two Sides DE , DF , each ...
... equal to two Sides of the other , each to each , and the Bafes equal , then the Angles contained under the equal Sides will be equal . LET the two Triangles be ABC , DEF , having two Sides , A B , AC , equal to two Sides DE , DF , each ...
Seite 12
... equal LE Parts . ET BAC be a given Right - lin❜d Angle , which is required to be cut into two equal Parts . Affume any Point D in the Right Line A B , and 3 of this , cut off AE from the Line AC equal to A D † ; join 1 of this , DE ...
... equal LE Parts . ET BAC be a given Right - lin❜d Angle , which is required to be cut into two equal Parts . Affume any Point D in the Right Line A B , and 3 of this , cut off AE from the Line AC equal to A D † ; join 1 of this , DE ...
Seite 14
... equal to H E , and HC is com- mon , GH and HC are each equal to E H and HC , and the Base CG is equal to the Bafe CE . Therefore 18 of this , the Angle CHG is equal to the Angle CHE ; and they are adjacent Angles . But when a Right Line ...
... equal to H E , and HC is com- mon , GH and HC are each equal to E H and HC , and the Base CG is equal to the Bafe CE . Therefore 18 of this , the Angle CHG is equal to the Angle CHE ; and they are adjacent Angles . But when a Right Line ...
Seite xxi
... equal to three others given : But it is requi- fite , that any two of the Right Lines taken to- gether be greater ... equal to A , B , C : Let there be one Right Line D E , ter- minated at D , but infinite towards E ; and take * DF * 3 ...
... equal to three others given : But it is requi- fite , that any two of the Right Lines taken to- gether be greater ... equal to A , B , C : Let there be one Right Line D E , ter- minated at D , but infinite towards E ; and take * DF * 3 ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2018 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2017 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
A B C adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle ABCD Circumference Cofine Cone confequently Coroll Cylinder defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fecond fhall be equal fimilar fince firft folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Reafon Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment ſhall Sides A B Sine Square Subtangent thefe THEOREM thofe thoſe tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe whoſe
Beliebte Passagen
Seite 195 - 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 165 - 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 169 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Seite xxii - ... 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 54 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 123 - GB is equal to E, and HD to F; GB and HD together are equal to E and F together : wherefore as many magnitudes as...
Seite 215 - 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...
Seite 196 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.
Seite 161 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Seite 207 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. V. The inclination of a straight line to a plane...