Manual of Euclid. Books IV. V. VI.1859 |
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Página 2
... rectilinear figure when the periphery of the circle touches all the sides of the figure . In the figure already given the circle is said to be inscribed in the greater square . Όρος 5 ' .— Κύκλος δὲ περὶ σχῆμα περιγράφεσθαι λέγεται ...
... rectilinear figure when the periphery of the circle touches all the sides of the figure . In the figure already given the circle is said to be inscribed in the greater square . Όρος 5 ' .— Κύκλος δὲ περὶ σχῆμα περιγράφεσθαι λέγεται ...
Página 66
... rectilinear figures are those which have their angles equal , one by one , and the sides about the equal angles proportional . DEFINITION II . Ὅρος β ́ . - Αντιπεπονθότα δὲ σχήματά ἐστιν , ὅταν ἑκατέρῳ τῶν σχημάτων ἡγούμενοί τε και ...
... rectilinear figures are those which have their angles equal , one by one , and the sides about the equal angles proportional . DEFINITION II . Ὅρος β ́ . - Αντιπεπονθότα δὲ σχήματά ἐστιν , ὅταν ἑκατέρῳ τῶν σχημάτων ἡγούμενοί τε και ...
Página 85
... rectilinear figure , similar to a given one , and similarly placed. ̧ Statement . Let AB - be the given straight line , and let GL be the given G figure . It is required to describe upon AB a figure similar to GL , and simi- F larly ...
... rectilinear figure , similar to a given one , and similarly placed. ̧ Statement . Let AB - be the given straight line , and let GL be the given G figure . It is required to describe upon AB a figure similar to GL , and simi- F larly ...
Página 89
... figure upon the second . PROPOSITION XXI . - THEOREM Πρότασις κα ' .- Τὰ τῷ αὐτῷ εὐθυγράμμῳ ὅμοια , καὶ ἀλλήλοις ἐστὶν ὅμοια . Figures similar to the same rectilinear figure are simi- lar to each other . Statement . Let each of the ...
... figure upon the second . PROPOSITION XXI . - THEOREM Πρότασις κα ' .- Τὰ τῷ αὐτῷ εὐθυγράμμῳ ὅμοια , καὶ ἀλλήλοις ἐστὶν ὅμοια . Figures similar to the same rectilinear figure are simi- lar to each other . Statement . Let each of the ...
Página 91
Euclid Joseph Allen Galbraith. AHMMA . LEMMA . - If rectilinear figures be equal and similar , their homologous sides ... figure RS is greater than N H T P R TN ( Prop . XX . ) ; but it is also equal to it , which is impossible ...
Euclid Joseph Allen Galbraith. AHMMA . LEMMA . - If rectilinear figures be equal and similar , their homologous sides ... figure RS is greater than N H T P R TN ( Prop . XX . ) ; but it is also equal to it , which is impossible ...
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Manual of Euclid: Books IV., V., VI., by J.A. Galbraith and S. Haughton Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
angle BAC angles ABC Annotation arc BC base BC is equal bisected centre circumscribed circle Corollary diameter draw drawn equal angles equal to F equi equiangular equilateral equimultiples exscribed circles find the locus fore fourth given circle given lines given point given ratio given straight lines given triangle greater ratio harmonically homologous sides inscribed intersection joining less mean proportional multiple parallel parallelogram perpendicular polygon Proof Prop Q. E. D. PROPOSITION quadrilateral radical axis radius rectangle rectilinear figure remaining angle right angle right line segments similar square Statement.-Let tangents tiple triangle ABC vertex vertical angle Wherefore αἱ ἀνάλογον δὲ δοθέντα ἐν ἔσται ἴσα ἰσάκις ἴσον καὶ κύκλον λόγον μεγέθη περὶ πλευραὶ πρὸς τὸ Πρότασις πρῶτον τὰ τὰς τὴν τῆς τοῖς τὸν αὐτὸν τοῦ τρίγωνα τῷ τῶν
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Página 38 - If the first be the same multiple of the second which the third is of the fourth, and if of the first and third there be taken equimultiples, these shall be equimultiples, the one of the second, and the other of the fourth. Let A the first be the same multiple of B the second, that C the third is of D the fourth ; and of A...
Página 28 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal...
Página 3 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Página 70 - DE ; but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Página 78 - CF ; but K has to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. Wherefore equiangular parallelograms, &c.
Página 71 - Now let BD be to DC, as BA to AC, and join AD ; the angle CAD is equal to the angle DAE. The same construction being made, because BD is to DC as BA to AC ; and also BD to DC, BA to AF (2.
Página 29 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Página 60 - D, and other four E, F, G, H, which, two and two, have the same ratio, viz. as A is to B, so is E to F; and as B...
Página 66 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less.
Página 68 - CF; and because it has been shewn, that, as the base BC is to the base CD, so is the triangle ABC to the triangle ACD; and as the triangle ABC is to the triangle ACD, so is the parallelogram EC to the parallelogram CF; therefore, as the base BC is to the base CD, so is the parallelogram EC to the parallelogram CF.