The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 Seiten |
Im Buch
Ergebnisse 1-5 von 74
Seite 2
... angle is that which is less than a right angle . XIII . " A term or boundary , is the extremity of any thing . " XIV . A figure is that which is inclofed by one or more boundaries . 1 XV . A circle is a plane figure contained THE ELEMENTS.
... angle is that which is less than a right angle . XIII . " A term or boundary , is the extremity of any thing . " XIV . A figure is that which is inclofed by one or more boundaries . 1 XV . A circle is a plane figure contained THE ELEMENTS.
Seite 6
... less than " two right angles , these straight lines being continually produc " ed shall at length meet upon that fide on which are the angles which are less than two right angles . See the notes on Prop , " 29. of Book I , ” T ...
... less than " two right angles , these straight lines being continually produc " ed shall at length meet upon that fide on which are the angles which are less than two right angles . See the notes on Prop , " 29. of Book I , ” T ...
Seite 10
... less , and join FC , GB . A Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is ...
... less , and join FC , GB . A Because AF is equal to AG , and AB to AC ; the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two tri- angles AFC , AGB ; therefore the base FC is ...
Seite 11
... less to the greater ; which is abfurd . There- fore AB is not unequal to AC , that is , it is equal to it . Wherefore if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is alfo equilateral . UPON PROP . VII . THEOR ...
... less to the greater ; which is abfurd . There- fore AB is not unequal to AC , that is , it is equal to it . Wherefore if two angles , & c . Q. E. D. B COR . Hence every equiangular triangle is alfo equilateral . UPON PROP . VII . THEOR ...
Seite 15
... less to the great- er ; which is impoffible . therefore two straight lines cannot have a A common fegment . To PROP . XII . PROB . E D B C O draw a straight line perpendicular to a given straight line of an unlimited length , from a ...
... less to the great- er ; which is impoffible . therefore two straight lines cannot have a A common fegment . To PROP . XII . PROB . E D B C O draw a straight line perpendicular to a given straight line of an unlimited length , from a ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Beliebte Passagen
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 163 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Seite 105 - 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. either the sides adjacent to the equal...
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Seite 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.