Manual of Euclid. Books IV. V. VI.1859 |
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Página 3
... radius AE describe a D 1 S circle ECF , and draw to either intersection of it with the given circle the line AC . Proof . This line is equal to AE by construction , and therefore to the given line D. PROPOSITION II . - PROBLEM ...
... radius AE describe a D 1 S circle ECF , and draw to either intersection of it with the given circle the line AC . Proof . This line is equal to AE by construction , and therefore to the given line D. PROPOSITION II . - PROBLEM ...
Página 5
... radius DF is inscribed in the given tri- angle . Draw DE and DG perpendicular to BA and AC . - B F Proof . In the triangles DEB , DFB , the angles DEB and DBE are equal to the angles DFB and DBF by construction , and the side DB is ...
... radius DF is inscribed in the given tri- angle . Draw DE and DG perpendicular to BA and AC . - B F Proof . In the triangles DEB , DFB , the angles DEB and DBE are equal to the angles DFB and DBF by construction , and the side DB is ...
Página 6
... radius of exscribed circle , and the triangle BCD , whose base is the third side , and altitude the same radius . Corollary 5. - From the preceding Corollary , and Corollary 4 ( II . 13 ) , we can express readily the radii of the three ...
... radius of exscribed circle , and the triangle BCD , whose base is the third side , and altitude the same radius . Corollary 5. - From the preceding Corollary , and Corollary 4 ( II . 13 ) , we can express readily the radii of the three ...
Página 7
... the centre F with the radius FA is circumscribed about the given triangle . Proof . In the triangles FDA , FDB , the sides DA and DB are equal by construction , FD is common to both , and the angles at D are right ; BOOK IV .
... the centre F with the radius FA is circumscribed about the given triangle . Proof . In the triangles FDA , FDB , the sides DA and DB are equal by construction , FD is common to both , and the angles at D are right ; BOOK IV .
Página 8
... radius FA passes through B and C , and therefore is circumscribed about the given triangle BAC . ΠΟΡΙΣΜΑ . COROLLARY . - If the centre F fall within the triangle , it is evident that all the angles are acute , for each of them is in a ...
... radius FA passes through B and C , and therefore is circumscribed about the given triangle BAC . ΠΟΡΙΣΜΑ . COROLLARY . - If the centre F fall within the triangle , it is evident that all the angles are acute , for each of them is in a ...
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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.