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 4
... which are not similar to one another , in the true sense of similarity received by all geometers ; and all these propositions have , for these reasons , been insufficiently demonstrated since Theon's time hitherto .
... which are not similar to one another , in the true sense of similarity received by all geometers ; and all these propositions have , for these reasons , been insufficiently demonstrated since Theon's time hitherto .
Seite 29
Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is ...
Seite 40
Ax . same reason , EF is equal to BC ; wherefore AD is equal b to EF , and DE is common ; therefore the whole , or the remainc 2. or 3. der AE , is equal < to the whole , or the remainder DF ; AB also Ax . is equal to DC ; and the two ...
Ax . same reason , EF is equal to BC ; wherefore AD is equal b to EF , and DE is common ; therefore the whole , or the remainc 2. or 3. der AE , is equal < to the whole , or the remainder DF ; AB also Ax . is equal to DC ; and the two ...
Seite 41
1 . because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH .
1 . because it is upon the same base BC , and between the same parallels BC , AD : for the like reason , the parallelogram EFGH is equal to the same EBCH : therefore also the parallelogram ABCD is equal to EFGH .
Seite 45
B G С lelogram , and AC its diame . ter , the triangle ABC is equal a to the triangle ADC : and a 34. 1 . because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equal to the triangle AHK : by the same reason ...
B G С lelogram , and AC its diame . ter , the triangle ABC is equal a to the triangle ADC : and a 34. 1 . because EKHA is a parallelogram , the diameter of which is AK , the triangle AEK is equal to the triangle AHK : by the same reason ...
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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 |