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 6
“ Equal and similar solid figures are “ those which are contained by similar planes of the same num“ ber and magnitude , ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be ...
“ Equal and similar solid figures are “ those which are contained by similar planes of the same num“ ber and magnitude , ” Now this proposition is a theorem , not a definition ; because the equality of figures of any kind must be ...
Seite 68
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . See N. TO find the centre of a given circle . Let ABC be the given circle ...
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . See N. TO find the centre of a given circle . Let ABC be the given circle ...
Seite 87
UPON the same straight line , and upon the same See N. side of it , there cannot be two similar segments of circles not coinciding with one another . If it be possible , let the two similar segments of circles , viz .
UPON the same straight line , and upon the same See N. side of it , there cannot be two similar segments of circles not coinciding with one another . If it be possible , let the two similar segments of circles , viz .
Seite 88
Wherefore , similar segments , & c . Q. E. D. PROP . XXV . PROB . See N. A SEGMENT of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment of a circle ; it is required to describe the ...
Wherefore , similar segments , & c . Q. E. D. PROP . XXV . PROB . See N. A SEGMENT of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment of a circle ; it is required to describe the ...
Seite 155
I. SIMILAR rectilineal figures Book VI . are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . II . Reciprocal figures , viz . triangles and parallelograms , are such See ...
I. SIMILAR rectilineal figures Book VI . are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . II . Reciprocal figures , viz . triangles and parallelograms , are such See ...
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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
added altitude angle ABC angle BAC base Book centre circle circle ABCD 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 Q. E. D. PROP radius reason rectangle rectangle contained 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 26 - Any two sides of a triangle are together greater than the third side.
Seite 60 - 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 26 - 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 55 - 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 24 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 161 - 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 15 - 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 187 - 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 35 - 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 176 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.