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, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Seite 19
Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . UPON the same base , and on the same side of it , See N. there cannot be two triangles that have their sides which are terminated in one extremity of the base ...
Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . UPON the same base , and on the same side of it , See N. there cannot be two triangles that have their sides which are terminated in one extremity of the base ...
Seite 103
... which is not greater than the diameter of the circle . Which was to be done . PROP . II . PROB . IN a given circle to inscribe a triangle equiangular . to a giyen triangle . Book IV . Let ABC be the given circle , OF EUCLID . 103.
... which is not greater than the diameter of the circle . Which was to be done . PROP . II . PROB . IN a given circle to inscribe a triangle equiangular . to a giyen triangle . Book IV . Let ABC be the given circle , OF EUCLID . 103.
Seite 104
1. is equald to the remaining angle EDF : wherefore the triangle ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . ... ABOUT a given circle to describe a triangle equi . angular to a given triangle .
1. is equald to the remaining angle EDF : wherefore the triangle ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . ... ABOUT a given circle to describe a triangle equi . angular to a given triangle .
Seite 105
1 . wherefore the triangle LMN is equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . G E PROP . IV . PROB . TO inscribe a circle in a given triangle ...
1 . wherefore the triangle LMN is equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . G E PROP . IV . PROB . TO inscribe a circle in a given triangle ...
Seite 111
TO inscribe an equilateral and equiangular pentagon in a given circle . Let ABCDE be the given circle ; it is required to inscribe an equilateral and equiangular pentagon in the circle ABCDE . Describe a an isosceles triangle FGH ...
TO inscribe an equilateral and equiangular pentagon in a given circle . Let ABCDE be the given circle ; it is required to inscribe an equilateral and equiangular pentagon in the circle ABCDE . Describe a an isosceles triangle FGH ...
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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Beliebte Passagen
Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografische Informationen
| Titel | 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, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Verlag | Mathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 518 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |