The College Euclid: Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities ... By A. K. Isbister1865 |
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Seite 7
... wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A a straight line AL ...
... wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A a straight line AL ...
Seite 9
... wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do ...
... wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do ...
Seite 12
... Wherefore , if two angles , & c . Cor . Hence every equiangular triangle is also equilaterai . Q. E. D. PROP . VII.- THEOREM . Upon the same base and on the same side of it , there cannot be two triangles that have their sides which are ...
... Wherefore , if two angles , & c . Cor . Hence every equiangular triangle is also equilaterai . Q. E. D. PROP . VII.- THEOREM . Upon the same base and on the same side of it , there cannot be two triangles that have their sides which are ...
Seite 14
... wherefore the angle FDC must likewise be greater than the angle BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to ᎠᏴ , therefore the angle BDC ...
... wherefore the angle FDC must likewise be greater than the angle BCD ; much more then must the angle BDC be greater than the angle BCD . Again , because in the triangle BCD , CB is assumed to be equal to ᎠᏴ , therefore the angle BDC ...
Seite 15
... wherefore BC coinciding with EF , BA and AC shall coincide with ED and DF ; for if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG , then ...
... wherefore BC coinciding with EF , BA and AC shall coincide with ED and DF ; for if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation as EG , FG , then ...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisect Book centre circle ABC circumference compounded constr DEMONSTRATION diameter double draw Edition English equal angles equal straight lines equal to BC equiangular equilateral and equiangular equimultiples Euclid exterior angle four magnitudes fourth French given circle given point given rectilineal angle given straight line gnomon Grammar greater ratio inscribed isosceles triangle join less Let ABC multiple opposite angles parallel parallelogram pentagon perpendicular plane polygon proportionals proposition Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment similar solid angle square of AC straight line AC THEOREM third three straight lines touches the circle triangle ABC twice the rectangle wherefore
Beliebte Passagen
Seite 140 - 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 xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 310 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Seite 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite vi - 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 on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Seite 310 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite xxxvii - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 69 - To divide a given straight line 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 287 - If any point be taken in the diameter of a circle which is not the centre, of all the straight lines which can be drawn from it to the circumference, the greatest is that in which the centre is, and the other part of that diameter is the least...