Manual of Euclid. Books IV. V. VI.1859 |
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Página 14
... BC , CD , and DE , Proof . Because each of the angles CAE and CEA is double of ECA by construction , and is bisected , the five angles CEB , BEA , ACE , CAD , and DAE , are equal , and therefore the arcs upon which they stand are equal ...
... BC , CD , and DE , Proof . Because each of the angles CAE and CEA is double of ECA by construction , and is bisected , the five angles CEB , BEA , ACE , CAD , and DAE , are equal , and therefore the arcs upon which they stand are equal ...
Página 21
... arc BC is bisected in L ) , or of oCA and LCB , but LCo is equal to the sum of LCB and oCB ; therefore oCA is equal oCB ; the angle ACB is therefore bisected by Co , and as Co ' is at right angles to oC ; Co ' bisects the angle below ...
... arc BC is bisected in L ) , or of oCA and LCB , but LCo is equal to the sum of LCB and oCB ; therefore oCA is equal oCB ; the angle ACB is therefore bisected by Co , and as Co ' is at right angles to oC ; Co ' bisects the angle below ...
Página 104
... arcs on which they stand ; so also have the sectors . PART I. Statement . Let ABC and DEF be equal circles ; and let BGC and EHF be angles at their centres , and BAC and EDF angles at their circumferences . The arc BC is to the arc EF ...
... arcs on which they stand ; so also have the sectors . PART I. Statement . Let ABC and DEF be equal circles ; and let BGC and EHF be angles at their centres , and BAC and EDF angles at their circumferences . The arc BC is to the arc EF ...
Página 105
... arc BC , and the angle BGC , have been taken equimultiples , viz . , the arc BL , and the angle BGL ; and of the arc EF , and of the angle EHF , any equimultiples whatever , viz . , the arc EN , and the angle EHN . And it has been ...
... arc BC , and the angle BGC , have been taken equimultiples , viz . , the arc BL , and the angle BGL ; and of the arc EF , and of the angle EHF , any equimultiples whatever , viz . , the arc EN , and the angle EHN . And it has been ...
Página 106
... arc BC , the same multiple is the sector BGL of the sector BGC . For the same reason , whatever multiple the arc EN is of the arc EF , the same multiple is the sector EHN of the sector EHF . If the arc BL be equal to the arc EN , the ...
... arc BC , the same multiple is the sector BGL of the sector BGC . For the same reason , whatever multiple the arc EN is of the arc EF , the same multiple is the sector EHN of the sector EHF . If the arc BL be equal to the arc EN , the ...
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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
Pasajes populares
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.