497:
it is convenient to make use of a little bit of
Cartesian geometry, although this of course was unavailable at the time." That sounds like a professor explaining it to a class. A similar reference to coordinate geometry is found in the first line of the section dealing with the volume of a sphere. The mathematical notation used in several of the sections is modern, not ancient Greek, and is clearly an attempt to explain Archimedes' work. Overall, this reads like a series of modern proofs to illustrate Archimedes' propositions, and is likely original research.
298:- Your link wasn't working but I found the page, while I am loathe to edit someones talk comment, I've fixed it for convenience. Unfortunately it's a rather poor article, with spelling errors in the title and calling him Aristotle near the end. The article does state that he argued against the actual infinite, but then goes on to describe how he used it firsthand. It is clear that he argued against it though, we describe modern use of the infinite excluding the actual as Archimedean. I'll try to dig up the source of this.
182:
466:"This type of method can be used to find the area of an arbitrary section of a parabola, and similar arguments can be used to find the integral of any power of x, although higher powers become complicated without algebra." that part of the text, this erroneous or incomplete, since neither arquimedes, nor any of the authors cited in the text say that, it would be good to cite that comment. to corroborate that information, or at least specify the types of buildings needed to reach what is this saying.
172:
151:
430:
flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result." Here it is clear that proofs aren't being gratuitously included. We are summarizing and explaining
Archimedes' method. We include a detailed explanation and proof of just one of the propositions. Two more are only sketched.
71:
53:
22:
81:
447:
raises a bright red flag. Either fix the proof or just be honest enough to say that you don't know. May I suggest either of the illustrious Dr. Michael Hardy or Dr. Arthur Rubin, provide a sound and "easy to follow" proof? I will check back in several weeks and see if either has been able to accomplish the task. May the odds be ever in your favour.
496:
The five sections which explain
Archimedes' propositions do not cite any sources. They read as if the editor has produced these proofs to illustrate how Archimedes' propositions work. For example, the first line in the section on the area of a parabola begins: "To explain Archimedes' method today,
429:
That's an essay that doesn't really summarize consensus of the math project. The style guide reads: "This is an encyclopedia, not a collection of mathematical texts; but we often want to include proofs to explain a theorem or definition. A downside of including proofs is that they may interrupt the
446:
The proof for the First proposition in the palimpsest is pathetic. It is by no means convincing and has large gaps in it. It is redundant to state that
Archimedes had to show that point I is the center of gravity of the triangle. I counted 3 uses of the word "suffices". To my superior mind, this
357:
Yes, that's the problem--- the work is being conflated with the most notable surviving copy. The palimpset is about the object, not the work itself. This page talks about the content of the work. Perhaps this could be "The Method of
Mechanical Theorems" or "Archimedes' Mechanical
260:
Some pages of the Method remained unused by the author of the
Palimpsest and then they are still -surely forever- lost. Between them, an annonced result was about the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakian have renamed
273:
between
Galileo and Cavalieri -ranging between years 1626 to around 1635- has as a main argument the hull and pyramid of the n=infinity dome. So in some sense it is true that the Method is only a theorem back from the modern infinitesimal theory.
386:"In particular, WP:NOTTEXTBOOK applies. If the proof can be found verbatim in any standard textbook on a subject, then it is better off transwikied to a project such as Wikibooks, Wikiversity, or ProofWiki.
238:
379:"Unlike textbooks, Knowledge does not strive to provide an axiomatic introduction to mathematics. Thus it is not necessary for a Knowledge article to prove every fact that is mentioned.
512:
I added "Original research" tags back in 2022; they were deleted by an IP editor in 2023. I"ve added the tag again, and this time I've listed this article at
550:
565:
545:
513:
228:
127:
560:
373:
133:
204:
555:
448:
286:
381:
Our best articles include references to good textbooks that the interested reader can consult for an axiomatic presentation of the field.
540:
408:
It’s the lack of citations for the proofs that is my concern. As far as I can tell, those proofs are not found in the text being cited.
481:
195:
156:
103:
521:
502:
413:
399:
94:
58:
33:
388:
There is also no point in presenting a novel proof not appearing before in print, because it falls afoul of WP:OR.
452:
21:
335:
is a disambiguation page. One of the items listed is "The Method of
Mechanical Theorems]], which directs to
517:
498:
409:
395:
344:
477:
287:
http://science-student.com/science-news/a-long-lost-text-by-achimedes-found-contains-some-work-on-calculus
435:
336:
290:
39:
181:
473:
469:
269:), whose volume relates to the n polygonal pyramid. This is amusing because the collaboration on
203:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
102:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
340:
303:
187:
525:
506:
485:
456:
417:
403:
367:
348:
326:
307:
293:
171:
150:
363:
322:
431:
289:
I can't work out how to put this in the article, but there it is for someone else to do so.
277:
See Apostol-Mnatsakanian in American Mathematical Monthly 111, June-July 2004 aditya kalra
534:
299:
86:
359:
318:
200:
70:
52:
332:
177:
76:
376:, here are two lengthy passages which I think have not been followed here:
285:
A citation for "Archimedes disbelieved in the use of infinitesimals" is
99:
317:
to "The Method", so it can be listed with the rest of his works.
15:
390:
These necessary conditions have not been very controversial"
199:, a collaborative effort to improve the coverage of
98:, a collaborative effort to improve the coverage of
132:This article has not yet received a rating on the
8:
19:
467:
145:
47:
442:Proof is far from clear or easy to follow
374:Knowledge:WikiProject Mathematics/Proofs
147:
49:
462:In the part of "the area of parabola"
7:
193:This article is within the scope of
92:This article is within the scope of
551:WikiProject Greece general articles
38:It is of interest to the following
14:
566:Low-priority mathematics articles
546:Unknown-importance Greek articles
213:Knowledge:WikiProject Mathematics
561:Start-Class mathematics articles
514:No Original Research Noticeboard
216:Template:WikiProject Mathematics
180:
170:
149:
79:
69:
51:
20:
233:This article has been rated as
492:Added "Original research" tags
1:
207:and see a list of open tasks.
106:and see a list of open tasks.
556:All WikiProject Greece pages
486:17:59, 23 October 2016 (UTC)
368:19:38, 10 January 2009 (UTC)
349:17:45, 10 January 2009 (UTC)
294:08:39, 23 October 2007 (UTC)
112:Knowledge:WikiProject Greece
507:02:00, 24 August 2022 (UTC)
327:16:48, 9 January 2009 (UTC)
115:Template:WikiProject Greece
582:
541:Start-Class Greek articles
134:project's importance scale
526:22:21, 14 June 2024 (UTC)
457:18:31, 17 June 2012 (UTC)
418:10:37, 22 June 2024 (UTC)
404:10:34, 22 June 2024 (UTC)
308:04:51, 27 June 2008 (UTC)
232:
165:
131:
64:
46:
313:Suggest moving this page
239:project's priority scale
196:WikiProject Mathematics
28:This article is rated
372:From the style guide
337:Archimedes Palimpsest
281:Use of infinitesimals
265:(and the half of it,
263:n=4 Archimedian Globe
267:n=4 Archimedian Dome
219:mathematics articles
518:Mr Serjeant Buzfuz
499:Mr Serjeant Buzfuz
410:Mr Serjeant Buzfuz
396:Mr Serjeant Buzfuz
188:Mathematics portal
95:WikiProject Greece
34:content assessment
488:
472:comment added by
253:
252:
249:
248:
245:
244:
144:
143:
140:
139:
573:
221:
220:
217:
214:
211:
190:
185:
184:
174:
167:
166:
161:
153:
146:
120:
119:
116:
113:
110:
89:
84:
83:
82:
73:
66:
65:
55:
48:
31:
25:
24:
16:
581:
580:
576:
575:
574:
572:
571:
570:
531:
530:
494:
464:
449:166.249.134.226
444:
315:
283:
258:
218:
215:
212:
209:
208:
186:
179:
159:
117:
114:
111:
108:
107:
85:
80:
78:
32:on Knowledge's
29:
12:
11:
5:
579:
577:
569:
568:
563:
558:
553:
548:
543:
533:
532:
529:
528:
493:
490:
463:
460:
443:
440:
427:
426:
425:
424:
423:
422:
421:
420:
393:
392:
391:
384:
352:
351:
314:
311:
282:
279:
257:
254:
251:
250:
247:
246:
243:
242:
231:
225:
224:
222:
205:the discussion
192:
191:
175:
163:
162:
154:
142:
141:
138:
137:
130:
124:
123:
121:
118:Greek articles
104:the discussion
91:
90:
74:
62:
61:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
578:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
538:
536:
527:
523:
519:
515:
511:
510:
509:
508:
504:
500:
491:
489:
487:
483:
479:
475:
471:
461:
459:
458:
454:
450:
441:
439:
437:
433:
419:
415:
411:
407:
406:
405:
401:
397:
394:
389:
385:
382:
378:
377:
375:
371:
370:
369:
365:
361:
356:
355:
354:
353:
350:
346:
342:
341:Michael Hardy
338:
334:
331:
330:
329:
328:
324:
320:
312:
310:
309:
305:
301:
296:
295:
292:
291:210.55.146.99
288:
280:
278:
275:
272:
268:
264:
255:
240:
236:
230:
227:
226:
223:
206:
202:
198:
197:
189:
183:
178:
176:
173:
169:
168:
164:
158:
155:
152:
148:
135:
129:
126:
125:
122:
105:
101:
97:
96:
88:
87:Greece portal
77:
75:
72:
68:
67:
63:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
495:
468:— Preceding
465:
445:
428:
387:
380:
316:
297:
284:
276:
271:indivisibles
270:
266:
262:
259:
235:Low-priority
234:
194:
160:Low‑priority
93:
40:WikiProjects
474:Sheldoniano
432:Tito Omburo
210:Mathematics
201:mathematics
157:Mathematics
30:Start-class
535:Categories
333:The Method
256:The Method
482:contribs
470:unsigned
358:Method"?
300:Nazlfrag
360:Likebox
319:Likebox
237:on the
109:Greece
100:Greece
59:Greece
36:scale.
522:talk
503:talk
478:talk
453:talk
436:talk
414:talk
400:talk
364:talk
345:talk
323:talk
304:talk
229:Low
128:???
537::
524:)
516:.
505:)
484:)
480:•
455:)
438:)
416:)
402:)
366:)
347:)
339:.
325:)
306:)
520:(
501:(
476:(
451:(
434:(
412:(
398:(
383:"
362:(
343:(
321:(
302:(
241:.
136:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.