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150:, Serenus deals largely with the areas of triangular sections of right and scalene cones that are created by planes passing through the vertex. He shows when the area of a triangle of a certain class of triangles is at its maximum. Propositions fifty-eight through sixty-nine form a separate section of the book and deal with the volumes of right cones in relation to their heights, their bases and the areas of triangular sections through the axis.
118:, Serenus states that his motivation for writing this work, as summarized by Heath, was that "many persons who were students of geometry were under the erroneous that the oblique section of a cylinder was different from the oblique section of a cone known as an ellipse, whereas it is of course the same curve." The work consists of thirty-three propositions.
98:
that the main result of the commentary was that of a number of angles that are subtended at a point on a diameter of a circle that is not the center, then with equal arcs of that circle, the angle nearer to the center is always less than the angle farther away from the center. But he was also a
125:
Proposition nine proves that the section by any plane not parallel to that of the bases or of one of the subcontrary sections but cutting all the generators is not a circle.
128:
Propositions fourteen and sixteen, the main results, are follow ups of the previous propositions where the said section is proved to have the property of the ellipse.
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Proposition six proves the existence an oblique cylinder of the parallel circular sections subcontrary to the series of which the bases are two.
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Proposition seventeen puts the property that was found in propositions fourteen and sixteen into the
Apollonian form using the
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on top of an older settlement. Two sources confirm that he was born in Antinoöpolis. It was once believed that he was born in
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Propositions twenty-nine to thirty-three deal with an optical problem. He gives a definition of
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prime mathematician in his own right, having written two works entitled
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223:, Biography in Dictionary of Scientific Biography (New York 1970-1990).
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at wilbourhall.org (text in German, Latin and
Ancient Greek)
111:. This connection helped them to survive through the ages.
83:, but this has been shown to have been based on an error.
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245:MacTutor History of Mathematics Archive
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1320:Latin translations of the 12th century
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94:, which is now lost. We hear from
86:Serenus wrote a commentary on the
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1352:A History of Greek Mathematics
865:The Quadrature of the Parabola
13:
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142:that was generally ridiculed.
1559:Ancient Greek mathematicians
1133:Intersecting secants theorem
258:On the Section of a Cylinder
116:On the Section of a Cylinder
101:On the Section of a Cylinder
40:; c. 300 – c. 360 AD) was a
7:
1128:Intersecting chords theorem
995:Doctrine of proportionality
10:
1595:
1579:4th-century mathematicians
824:On the Sphere and Cylinder
777:On the Sizes and Distances
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1526:Ancient Greece portal
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1330:Philosophy of mathematics
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1245:Ptolemy's table of chords
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300:Ancient Greek mathematics
240:"Serenus of Antinoöpolis"
63:Serenus came either from
1197:Aristarchus's inequality
770:On Conoids and Spheroids
262:On the Section of a Cone
250:University of St Andrews
153:
148:On the Section of a Cone
105:On the Section of a Cone
1305:Ancient Greek astronomy
1118:Inscribed angle theorem
1108:Greek geometric algebra
763:Measurement of a Circle
28:Serenus of Antinoöpolis
1539:Mathematics portal
1325:Non-Euclidean geometry
1280:Mouseion of Alexandria
1153:Tangent-secant theorem
1103:Geometric mean theorem
1088:Exterior angle theorem
1083:Angle bisector theorem
787:On Sizes and Distances
206:. Dover publications.
18:Serenus of Antinouplis
1227:Pappus's area theorem
1163:Theorem of the gnomon
1040:Quadratrix of Hippias
963:Circles of Apollonius
911:Problem of Apollonius
889:Constructible numbers
713:Archimedes Palimpsest
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1443:prehistoric counting
1240:Ptolemy's inequality
1181:Apollonius's theorem
1020:Method of exhaustion
990:Diophantine equation
980:Circumscribed circle
797:On the Moving Sphere
236:Robertson, Edmund F.
200:Heath, Thomas Little
1529: •
1335:Neusis construction
1255:Spiral of Theodorus
1148:Pythagorean theorem
1093:Euclidean algorithm
1035:Lune of Hippocrates
904:Squaring the circle
660:Theon of Alexandria
335:Aristaeus the Elder
234:O'Connor, John J.;
185:Heath p. 520 (1981)
169:Heath p. 519 (1981)
96:Theon of Alexandria
42:Greek mathematician
1222:Menelaus's theorem
1212:Irrational numbers
1025:Parallel postulate
1000:Euclidean geometry
968:Apollonian circles
510:Isidore of Miletus
221:Ivor Bulmer-Thomas
114:In the preface of
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1250:Ptolemy's theorem
1123:Intercept theorem
973:Apollonian gasket
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872:The Sand Reckoner
16:(Redirected from
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1564:Roman-era Greeks
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1285:Platonic Academy
1232:Problem II.8 of
1202:Crossbar theorem
1158:Thales's theorem
1098:Euclid's theorem
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1217:Law of sines
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71:, a city in
69:Antinoöpolis
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46:Late Antique
27:
26:
1426:mathematics
1234:Arithmetica
831:Ostomachion
800:(Autolycus)
719:Arithmetica
495:Hippocrates
425:Dinostratus
410:Dicaearchus
340:Aristarchus
75:founded by
53:Roman Egypt
1574:360 deaths
1569:300 births
1553:Categories
1478:Babylonian
1378:arithmetic
1344:History of
1173:Apollonius
858:(Menelaus)
817:On Spirals
736:Catoptrics
675:Xenocrates
670:Thymaridas
655:Theodosius
640:Theaetetus
620:Simplicius
610:Pythagoras
595:Posidonius
580:Philonides
540:Nicomachus
535:Metrodorus
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480:Hipparchus
470:Heliodorus
420:Diophantus
405:Democritus
385:Chrysippus
355:Archimedes
350:Apollonius
320:Anaxagoras
312:(timeline)
193:References
92:Apollonius
939:Inscribed
699:Treatises
690:Zenodorus
650:Theodorus
625:Sosigenes
570:Philolaus
555:Oenopides
550:Nicoteles
545:Nicomedes
505:Hypsicles
400:Ctesibius
390:Cleomedes
375:Callippus
360:Autolycus
345:Aristotle
325:Anthemius
140:parallels
65:Antinoeia
44:from the
1503:Japanese
1488:Egyptian
1431:timeline
1419:timeline
1407:timeline
1402:geometry
1395:timeline
1390:calculus
1383:timeline
1371:timeline
1074:Elements
920:Concepts
882:Problems
855:Spherics
845:Spherics
810:(Euclid)
756:(Euclid)
753:Elements
746:(Euclid)
707:Almagest
615:Serenus
590:Porphyry
530:Menelaus
485:Hippasus
460:Eutocius
435:Domninus
330:Archytas
202:(1981).
67:or from
1483:Chinese
1438:numbers
1366:algebra
1294:Related
1268:Centers
1064:Results
934:Central
605:Ptolemy
600:Proclus
565:Perseus
520:Marinus
500:Hypatia
490:Hippias
465:Geminus
455:Eudoxus
445:Eudemus
415:Diocles
81:Antissa
77:Hadrian
49:Thebaid
37:Σερῆνος
1498:Indian
1275:Cyrene
807:Optics
726:Conics
645:Theano
635:Thales
630:Sporus
575:Philon
560:Pappus
450:Euclid
380:Carpus
370:Bryson
210:
109:Conics
88:Conics
1493:Incan
1414:logic
1190:Other
958:Chord
951:Axiom
929:Angle
585:Plato
475:Heron
395:Conon
154:Notes
73:Egypt
32:Greek
1455:list
743:Data
515:Leon
365:Bion
260:and
208:ISBN
103:and
1357:by
1071:In
90:of
51:in
1555::
248:,
242:,
238:,
174:^
162:^
55:.
34::
292:e
285:t
278:v
216:.
135:.
30:(
20:)
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