By Morris Kline

ISBN-10: 019503533X

ISBN-13: 9780195035339

ISBN-10: 0195042301

ISBN-13: 9780195042306

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Download e-book for kindle: Calculus: An Intuitive and Physical Approach (2nd Edition) by Morris Kline

Application-oriented creation relates the topic as heavily as attainable to technology. In-depth explorations of the spinoff, the differentiation and integration of the powers of x, theorems on differentiation and antidifferentiation, the chain rule and examinations of trigonometric features, logarithmic and exponential services, ideas of integration, polar coordinates, even more.

Download e-book for kindle: Spectral Representations for Schradinger Operators with by Lee John Skandalakis, John E. Skandalakis, Panajiotis N.

The good fortune of any operative approach depends, partly, at the surgeon’s wisdom of anatomy. From the 1st incision to closure of the wound, it really is necessary to comprehend the fascial layers, blood offer, lymphatic drainage, nerves, muscular tissues and organs appropriate to the operative strategy. Surgical Anatomy and strategy: A Pocket guide covers the anatomic areas pertinent to normal surgeons and in addition describes the main normally played common surgical options.

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S ✐st ✉♥❛❜❤ä♥❣✐❣ ✈♦♥ ❞❡r ❲❛❤❧ ✈♦♥  ✉♥❞ & ✳ ❆❧❧❣❡♠❡✐♥ ❣❡❧t❡♥ ❢ür ❛✉s❣❡✇ä❤❧t❡ ■♥t❡r✈❛❧❧❡ ❢♦❧❣❡♥❞❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥  $ !  ❉✐❡ ■♥t❡r✈❛❧❧❡ 
& & ❤❡✐ÿ❡♥ & ✲■♥t❡r✈❛❧❧❡ ✉♥❞ ❣❡❜❡♥ ❡✐♥❡ ❣r♦❜❡ ■♥❢♦r♠❛t✐♦♥ ü❜❡r ❞✐❡ ❱❡rt❡✐❧✉♥❣ ❞❡r ❲❡rt❡ ❞❡r ❩✉❢❛❧❧s❣röÿ❡✳ ✶✳✶✵✳✷ ◆♦r♠❛❧✈❡rt❡✐❧t❡ ❆❦t✐❡♥❦✉rs❡ ■♥ ✈✐❡❧❡♥ ❋ä❧❧❡♥ ✐st ❞✐❡ ❱❡rt❡✐❧✉♥❣ ✈♦♥ ❆❦t✐❡♥r❡♥❞✐t❡♥✱ ✇✐❡ ❞✐❡ ❞❡r ✐♥ ❇❡✐s♣✐❡❧ ✶✳✽✳✹ ✉♥t❡rs✉❝❤t❡♥ ❆❞✐❞❛s✲❆❦t✐❡✱ ♥ä❤❡r✉♥❣s✇❡✐s❡ ❡✐♥❡ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣✳ ▲❡❣t ♠❛♥ ❞✐❡ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ❛❧s ▼♦❞❡❧❧ ❢ür ❞✐❡ ❱❡rt❡✐❧✉♥❣ ✈♦♥ ❆❦t✐❡♥r❡♥❞✐t❡♥ ③✉❣r✉♥❞❡✱ s✐♥❞ ❆✉ss❛❣❡♥ ü❜❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥ ❞❛rü❜❡r✱ ♦❜ ❡✐♥❡ ❜❡❧✐❡❜✐❣❡ ❘❡♥❞✐t❡ ✐♥ ❡✐♥ ❜❡✲ st✐♠♠t❡s ■♥t❡r✈❛❧❧ ❢ä❧❧t✱ ♠ö❣❧✐❝❤✳ ❇❡✐s♣✐❡❧ ✶✳✶✵✳✹ ✭▼♦❞❡❧❧✐❡r✉♥❣ ❡✐♥❡s ❆❦t✐❡♥❦✉rs❡s ♠✐tt❡❧s ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣✮✳ ■♠ ❇❡✐s♣✐❡❧ ✶✳✽✳✹ ✇✉r❞❡♥ ❞✐❡ ❘❡♥❞✐t❡♥ ❞❡r ❆❞✐❞❛s✲❆❦t✐❡ ✐♠ ❩❡✐tr❛✉♠ ✈♦♥ ❏✉♥✐ ✵✼ ❜✐s ▼❛✐ ✵✽ ✉♥t❡rs✉❝❤t✳ ❯♥t❡r ❞❡r ❆♥♥❛❤♠❡✱ ❞❛ss ❞✐❡ ✇ö❝❤❡♥t❧✐❝❤❡ ❘❡♥❞✐t❡  ❡✐♥❡ ♥♦r✲ ♠❛❧✈❡rt❡✐❧t❡ ❩✉❢❛❧❧s❣röÿ❡ ✐st✱ ❜✐❧❞❡♥ ❞✐❡ ✐♠ ❇❡✐s♣✐❡❧ ✶✳✽✳✹ ❛♥❣❡❣❡❜❡♥❡♥ ❑❡♥♥❣röÿ❡♥ ❉r✐❢t  ✉♥❞ ❱♦❧❛t✐❧✐tät % ❙❝❤ät③✇❡rt❡ ❢ür ❞❡♥ ❊r✇❛rt✉♥❣s✇❡rt  ✉♥❞ ❞✐❡ ❙t❛♥❞❛r❞❛❜✲ & ✳ ❲✐r ♥❡❤♠❡♥ ❛❧s♦ ❛♥✱ ❞❛ss  ♥♦r♠❛❧✈❡rt❡✐❧t ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ ✵✱✵✵✹✾ ✇❡✐❝❤✉♥❣ ✷ ✉♥❞ ✵✱✵✷✹✻ ✐st✳ ❉✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ❞❛❢ür✱ ❞❛ss ❡✐♥❡ ❜❡❧✐❡❜✐❣❡ ❲♦❝❤❡♥r❡♥❞✐t❡ ③✇✐s❝❤❡♥ ✲✵✱✵✵✶✼ ✉♥❞ ✵✱✵✶✵✻ ❧✐❡❣t✱ ❜❡trä❣t     $ $$ $ $$ $ $$ $ $$ 
$ $$  $ $$     $ $" $ $"  $  ❉❡r ❱❡r❣❧❡✐❝❤ ❞✐❡s❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ♠✐t ❞❡r t❛tsä❝❤❧✐❝❤ ❛✉❢❣❡tr❡t❡♥❡♥ r❡❧❛t✐✈❡♥ ❍ä✉✜❣❦❡✐t ✈♦♥ ✵✱✷✵ ③❡✐❣t ❡✐♥❡ ❛♥♥ä❤❡r♥❞❡ Ü❜❡r❡✐♥st✐♠♠✉♥❣✳ ❉✐❡s❡ ❆✉ss❛❣❡ tr✐✛t ❛✉❝❤ ❢ür ❛♥❞❡r❡ ❘❡♥❞✐t❡❜❡r❡✐❝❤❡ ③✉✱ ✇✐❡ ❚❛❜❡❧❧❡ ✶✳✽ ③❡✐❣t✳ ❉✐❡ ■♥t❡r♣r❡t❛t✐♦♥ ❞❡s ❩✉s❛♠♠❡♥❤❛♥❣❡s ③✇✐s❝❤❡♥ ❞❡♥ ❜❡♦❜❛❝❤t❡t❡♥ ❑❡♥♥❣röÿ❡♥ ✉♥❞ ❞❡♥ ♠♦❞❡❧❧✐❡rt❡♥ P❛r❛♠❡t❡r♥ ❞❡r ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ❜❡r✉❤t ❛✉❢ ❞❡♠ ●❡s❡t③ ❞❡r ❣r♦ÿ❡♥ ❩❛❤❧❡♥✿ ❉❛s ❛r✐t❤♠❡t✐s❝❤❡ ▼✐tt❡❧ ❛✉s ✈✐❡❧❡♥ ❇❡♦❜❛❝❤t✉♥❣❡♥ ❡✐♥❡r ❩✉❢❛❧❧s❣rö✲ ÿ❡ ❧✐❡❣t ♥❛❤❡ ❞❡♠ ❊r✇❛rt✉♥❣s✇❡rt ✉♥❞ ❞✐❡ ❙t❛♥❞❛r❞❛❜✇❡✐❝❤✉♥❣ ❞❡r ❜❡♦❜❛❝❤t❡t❡♥ ❲❡rt❡ ♥❛❤❡ & ✳ ❯♠❣❡❦❡❤rt s✐♥❞ ❛r✐t❤♠❡t✐s❝❤❡s ▼✐tt❡❧ ✉♥❞ ❡♠♣✐r✐s❝❤❡ ❙t❛♥❞❛r❞❛❜✲ ✇❡✐❝❤✉♥❣ ❛✉s ✈✐❡❧❡♥ ✉♥❛❜❤ä♥❣✐❣❡♥ ❇❡♦❜❛❝❤t✉♥❣❡♥ ❡✐♥❡r ❩✉❢❛❧❧s❣röÿ❡ ❙❝❤ät③✇❡rt❡ ❢ür ❞❡r❡♥ ❊r✇❛rt✉♥❣s✇❡rt ✉♥❞ ❱❛r✐❛♥③✳ ✶✳✶✶✳ ❲■❊◆❊❘✲P❘❖❩❊❙❙ ✸✶ ❘❡♥❞✐t❡❜❡r❡✐❝❤ ❘❡❧❛t✐✈❡ ❍ä✉✜❣❦❡✐t ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t  ✮ ✭❣❡r✉♥❞❡t✮ 
    
  ❀   ✵✱✵✷ ✵✱✵✸ 
  ❀   ✵✱✵✽ ✵✱✵✻ 
  ❀    ✵✱✶✻ ✵✱✶✶ 
   ❀    ✵✱✶✹ ✵✱✶✼ 
   ❀    ✵✱✷✵ ✵✱✷✵ 
   ❀    ✵✱✶✻ ✵✱✶✽ ✵✱✶✷ ✵✱✶✷ 
  ❀   
  ❀   ✵✱✶✵ ✵✱✵✼ 
  ❀    ✵✱✵✹ ✵✱✵✸ ❚❛❜✳ ✶✳✽✿ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥ ✉♥❞ r❡❧❛t✐✈❡ ❍ä✉✜❣❦❡✐t❡♥ ❢ür ❘❡♥❞✐t❡❜❡r❡✐❝❤❡ ✉♥t❡r ❞❡r ❆♥♥❛❤♠❡ ❡✐♥❡r ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ❞❡r ❘❡♥❞✐t❡♥ ✶✳✶✶ ❲✐❡♥❡r✲Pr♦③❡ss ■♠ ❏❛❤r❡ ✶✽✷✼ ❜❡♦❜❛❝❤t❡t❡ ❞❡r s❝❤♦tt✐s❝❤❡ ❇♦t❛♥✐❦❡r ❘♦❜❡rt ❇r♦✇♥ ✭✶✼✼✸✕✶✽✺✽✮ ✉♥t❡r ❡✐♥❡♠ ▼✐❦r♦s❦♦♣✱ ✇✐❡ s✐❝❤ ❇❧üt❡♥♣♦❧❧❡♥ ✐♥ ❡✐♥❡♠ ❲❛ss❡rtr♦♣❢❡♥ ✉♥r❡❣❡❧♠ä✲ ÿ✐❣ ❤✐♥✲ ✉♥❞ ❤❡r❜❡✇❡❣❡♥✳ ❉✐❡s❡ s♦ ❣❡♥❛♥♥t❡ ❇r♦✇♥s❝❤❡ ▼♦❧❡❦✉❧❛r❜❡✇❡❣✉♥❣ ❡✐♥❡s ❚❡✐❧❝❤❡♥s ✐st ❛✉❢ ❡✐♥❡ stä♥❞✐❣❡ ❑♦❧❧✐s✐♦♥ ③✇✐s❝❤❡♥ ❞❡♥ ❇❧üt❡♥♣♦❧❧❡♥ ✉♥❞ ❞❡♥ s✐❝❤ ❜❡✇❡❣❡♥❞❡♥ ❲❛ss❡r♠♦❧❡❦ü❧❡♥ ③✉rü❝❦③✉❢ü❤r❡♥✳ ◆❛❝❤❞❡♠ ✐♠ ❏❛❤r❡ ✶✾✵✺ ❆❧❜❡rt ❊✐♥✲ st❡✐♥ ✭✶✽✼✾✕✶✾✺✺✮ ❞✐❡s❡ ♣❤②s✐❦❛❧✐s❝❤❡ ❊r❦❧är✉♥❣ ❢ür ❞✐❡ ❇r♦✇♥s❝❤❡ ▼♦❧❡❦✉❧❛r❜❡✲ ✇❡❣✉♥❣ ❧✐❡❢❡rt❡✱ ❣❡❧❛♥❣ ❡s ❞❡♠ ❯❙✲❛♠❡r✐❦❛♥✐s❝❤❡♥ ▼❛t❤❡♠❛t✐❦❡r ◆♦r❜❡rt ❲✐❡♥❡r ✭✶✽✾✹✕✶✾✻✹✮ ✐♠ ❏❛❤r❡ ✶✾✷✸ ❞❛s P❤ä♥♦♠❡♥ ❛✉❝❤ ♠❛t❤❡♠❛t✐s❝❤ ❛❧s ❡✐♥❡♥ st♦❝❤❛s✲ t✐s❝❤❡♥ Pr♦③❡ss ③✉ ❜❡s❝❤r❡✐❜❡♥✳ ❉❛❜❡✐ ❧ässt s✐❝❤ ❞✐❡ ③❡✐t❧✐❝❤❡ ❊♥t✇✐❝❦❧✉♥❣ ❡♥t❧❛♥❣ ❥❡❞❡r ❑♦♦r❞✐♥❛t❡ ♠✐t ❞❡♥ ●❡s❡t③❡♥ ❡✐♥❡s ❲✐❡♥❡r✲Pr♦③❡ss❡s ❡r❦❧är❡♥✳ ❉❡r ❲✐❡♥❡r✲ Pr♦③❡ss s♣✐❡❧t ❞✐❡ ③❡♥tr❛❧❡ ❘♦❧❧❡ ✐♠ ❑❛❧❦ü❧ ③❡✐tst❡t✐❣❡r st♦❝❤❛st✐s❝❤❡r Pr♦③❡ss❡ ✉♥❞ ✇✐r❞ ✐♥ ③❛❤❧❧♦s❡♥ ●❡❜✐❡t❡♥ ❞❡r ◆❛t✉r✲ ✉♥❞ ❲✐rts❝❤❛❢ts✇✐ss❡♥s❝❤❛❢t❡♥ ❛❧s ●r✉♥❞❧❛❣❡ ③✉r ❙✐♠✉❧❛t✐♦♥ ③✉❢ä❧❧✐❣❡r ❇❡✇❡❣✉♥❣❡♥ ❤❡r❛♥❣❡③♦❣❡♥✳ ❉❡✜♥✐t✐♦♥ ✶✳✶✶✳✶ ✭❲✐❡♥❡r✲Pr♦③❡ss✮✳ ❉❡r ❲✐❡♥❡r✲Pr♦③❡ss   ✐st ❡✐♥❡ ❋❛✲  ♠✐❧✐❡ ✈♦♥ ❩✉❢❛❧❧s❣röÿ❡♥✱ ❞✐❡ ❞✉r❝❤ ❢♦❧❣❡♥❞❡ ❊✐❣❡♥s❝❤❛❢t❡♥ ❝❤❛r❛❦t❡r✐s✐❡rt s✐♥❞✿ ❊✶   $ ❊✷ ❊✸ ❋ür $ %  ' ✐st   ❡✐♥❡ ♥♦r♠❛❧✈❡rt❡✐❧t❡ ❩✉❢❛❧❧s❣röÿ❡ ♠✐t ❞❡♠ ❊r✇❛rt✉♥❣s✇❡rt ✵ ✉♥❞ ❞❡r ❱❛r✐❛♥③ ' %✳ ❋ür ❜❡❧✐❡❜✐❣❡ $ #  % '  ( s✐♥❞ ❞✐❡ ❩✉❢❛❧❧s❣röÿ❡♥ !

R ❡r❤❛❧t❡♥ ❢ür ! ✉♥❞  ✉♥t❡r ◆✉t③✉♥❣ ✈♦♥ ●❧❡✐❝❤✉♥❣ ✶✳✺ !   '  (  & ! '  &   (  & !   ◆❛❝❤ ❊✐❣❡♥s❝❤❛❢t ❊✷ ❞❡s ❲✐❡♥❡r✲Pr♦③❡ss❡s ✐st & !   ❡✐♥❡ ♥♦r♠❛❧✈❡rt❡✐❧t❡   ❩✉❢❛❧❧s❣röÿ❡ ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ $ ✉♥❞ &  (✳ ❉❛♠✐t ✐st ❞✐❡ ❘❡♥❞✐t❡  !

P■❚❊▲ ✶✳ ❆❑❚■❊◆ ❉✐❡ ❡rst❡ ❊✐❣❡♥s❝❤❛❢t s✐❝❤❡rt ✉♥s✱ ❞❛ss ❞❡r Pr♦③❡ss ✐♠ ❯rs♣r✉♥❣ ❞❡s ❑♦♦r❞✐♥❛t❡♥✲ s②st❡♠s ❜❡❣✐♥♥t✳ ❉✐❡ ③✇❡✐t❡ ❊✐❣❡♥s❝❤❛❢t ❜❡s❛❣t✱ ❞❛ss ❞✐❡ P♦s✐t✐♦♥sä♥❞❡r✉♥❣   ❞❡s ❚❡✐❧❝❤❡♥s s♦✇♦❤❧ ✐♥ *✲ ❛❧s ❛✉❝❤ ✐♥ + ✲❘✐❝❤t✉♥❣ ❡✐♥❡ ♥♦r♠❛❧✈❡rt❡✐❧t❡ ❩✉❢❛❧❧s❣röÿ❡ ♠✐t ❞❡♠ ❊r✇❛rt✉♥❣s✇❡rt $ ✉♥❞ ❞❡r ❱❛r✐❛♥③ ' % ✐st✳ ❉✐❡ ❱❛r✐❛♥③ ❞❡r ③✉❢ä❧❧✐❣❡♥ P♦s✐t✐♦♥sä♥❞❡r✉♥❣ ❤ä♥❣t ❞❛❜❡✐ ♥✉r ✈♦♥ ❞❡r ▲ä♥❣❡ ❞❡s ❩❡✐t✐♥t❡r✈❛❧❧s ' % ✉♥❞ ♥✐❝❤t ✈♦♥ ❞❡r P♦s✐t✐♦♥     ❞❡s ❚❡✐❧❝❤❡♥s ③✉r ❩❡✐t % ❛❜✳ ❉✐❡ ❇❡✇❡❣✉♥❣❡♥ ❞❡s ❚❡✐❧❝❤❡♥s ✐♥ *✲ ✉♥❞ + ✲❘✐❝❤t✉♥❣ s✐♥❞ ❞❛❜❡✐ ✉♥❛❜❤ä♥❣✐❣ ✈♦♥❡✐♥❛♥❞❡r✳ ❉✐❡ ❞r✐tt❡ ❊✐❣❡♥s❝❤❛❢t ✈❡r❞❡✉t❧✐❝❤t✱ ❞❛ss ❞✐❡ P♦s✐t✐♦♥sä♥❞❡r✉♥❣❡♥ ✐♥ s✐❝❤ ♥✐❝❤t ü❜❡r❧❛♣♣❡♥❞❡♥ ❩❡✐t✐♥t❡r✈❛❧✲ ❧❡♥ ✉♥❛❜❤ä♥❣✐❣ ✈♦♥❡✐♥❛♥❞❡r s✐♥❞✳ ❆✉❢ ❞✐❡ ❇r♦✇♥s❝❤❡ ❇❡✇❡❣✉♥❣ ❜❡③♦❣❡♥ ❜❡❞❡✉t❡t ❞✐❡s✱ ❞❛ss ❦❡✐♥❡ ❙❝❤❧üss❡ ü❜❡r ❞✐❡ ❘✐❝❤t✉♥❣ ✉♥❞ ●röÿ❡ ❞❡r P♦s✐t✐♦♥sä♥❞❡r✉♥❣❡♥ ❛✉s ❞❡♥ ✈♦r❛♥❣❡❣❛♥❣❡♥❡♥ ❚❡✐❧❝❤❡♥❜❡✇❡❣✉♥❣❡♥ ♠ö❣❧✐❝❤ s✐♥❞✳ ❱♦r❤❡r✐❣❡ P♦s✐t✐♦♥sä♥❞❡✲ r✉♥❣❡♥ ❜❡❡✐♥✢✉ss❡♥ ❢♦❧❣❡♥❞❡ P♦s✐t✐♦♥sä♥❞❡r✉♥❣❡♥ ♥✐❝❤t✳ ❉✐❡ P♦s✐t✐♦♥sä♥❞❡r✉♥❣❡♥   ✇❡r❞❡♥ ❛✉❝❤ ❩✉✇ä❝❤s❡ ❣❡♥❛♥♥t✳ ❉✐❡s❡ ❦ö♥♥❡♥ s♦✇♦❤❧ ♣♦s✐t✐✈❡ ❛❧s ❛✉❝❤ ♥❡❣❛t✐✈❡ ❲❡rt❡ ❛♥♥❡❤♠❡♥✳ ✶✳✶✷ ❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦❞❡❧❧ ❢ür ❆❦t✐❡♥❦✉rs♣r♦③❡ss❡ ❉❛s ❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦❞❡❧❧ ✐st ❡❜❡♥s♦ ✇✐❡ ❞❛s ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ✭❑❛♣✐t❡❧ ✶✳✾✮ ❡✐♥ ♠❛t❤❡♠❛t✐s❝❤❡s ▼♦❞❡❧❧ ③✉r ❇❡s❝❤r❡✐❜✉♥❣ ✈♦♥ ❆❦t✐❡♥❦✉rs♣r♦③❡ss❡♥✳ ❉❛s ❇❧❛❝❦✲ ❙❝❤♦❧❡s✲▼♦❞❡❧❧ ❜❛s✐❡rt ❛✉❢ ❞❡r ❆♥♥❛❤♠❡✱ ❞❛ss s✐❝❤ ❞❡r st♦❝❤❛st✐s❝❤❡ Pr♦③❡ss ❞❡r ❘❡♥❞✐t❡❡♥t✇✐❝❦❧✉♥❣ ❛✉s ❡✐♥❡♠ ❞❡t❡r♠✐♥✐st✐s❝❤❡♥ ③❡✐t❧✐❝❤ ❧✐♥❡❛r❡♥ ✉♥❞ ❡✐♥❡♠ ③✉❢ä❧✲ ❧✐❣❡♥ ❆♥t❡✐❧ ③✉s❛♠♠❡♥s❡t③t✳ ❉❡r ❞❡t❡r♠✐♥✐st✐s❝❤❡ ❆♥t❡✐❧ ❞❡s ❘❡♥❞✐t❡♣r♦③❡ss❡s ❧ässt s✐❝❤ ❛❧s ❡r✇❛rt❡t❡ ❘❡♥❞✐t❡ ✐♥t❡r♣r❡t✐❡r❡♥✳ ❆❦t✐❡♥❦✉rs❡ ❢♦❧❣❡♥ ❥❡❞♦❝❤ ❦❡✐♥❡♠ ❞❡t❡r♠✐✲ ♥✐st✐s❝❤❡♥ ▼✉st❡r✱ s♦♥❞❡r♥ ✈♦❧❧❢ü❤r❡♥ ❡✐♥❡ ③✉❢ä❧❧✐❣❡ ■rr❢❛❤rt ✭✈❣❧✳ ✶✳✾✮✳ ❉❡♠♥❛❝❤ ✉♥✲ t❡r❧✐❡❣❡♥ ❘❡♥❞✐t❡♥ ❡❜❡♥❢❛❧❧s ❡✐♥❡♠ st♦❝❤❛st✐s❝❤❡♥ Pr♦③❡ss✱ ❞❡r ❞✉r❝❤ ❞❡♥ ③✉❢ä❧❧✐❣❡♥ ❆♥t❡✐❧ ❜❡s❝❤r✐❡❜❡♥ ✇✐r❞✳ ❉❛❜❡✐ ✇✐r❞ ❛♥❣❡♥♦♠♠❡♥✱ ❞❛ss ❞❡r st♦❝❤❛st✐s❝❤❡ Pr♦③❡ss ❞❡r ❧♦❣❛r✐t❤♠✐s❝❤❡♥ ❘❡♥❞✐t❡♥ ❡✐♥❡♠ ❲✐❡♥❡r✲Pr♦③❡ss ❢♦❧❣t✳ ❉❡✜♥✐t✐♦♥ ✶✳✶✷✳✶ ✭❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦❞❡❧❧✮✳ ❋ür ❞❡♥ st♦❝❤❛st✐s❝❤❡♥ Pr♦③❡ss ❞❡r ❘❡♥❞✐t❡❡♥t✇✐❝❦❧✉♥❣ ✇✐r❞ ❛♥❣❡♥♦♠♠❡♥✱ ❞❛ss   '  & ✭✶✳✺✮ ✐st✳ ❉❛❜❡✐ s✐♥❞ ' $✱   ✉♥❞ &  $✳ ❉❛rü❜❡r ❤✐♥❛✉s s✐♥❞  ✉♥❞ & ❦♦♥st❛♥t✳ ▼✐t ❞❡♠ ❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦❞❡❧❧ ❦❛♥♥ ❞✐❡ ❱❡rt❡✐❧✉♥❣ ❞❡r ❘❡♥❞✐t❡  ❜❡st✐♠♠t ✇❡r✲ ❞❡♥✳ ◆❛❝❤ ❞❡r ③✇❡✐t❡♥ ❊✐❣❡♥s❝❤❛❢t ❞❡s ❲✐❡♥❡r✲Pr♦③❡ss❡s ✉♥❞ ✇❡❣❡♥   $ ✐st ❞✐❡ ❩✉❢❛❧❧s❣röÿ❡     ♥♦r♠❛❧✈❡rt❡✐❧t ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ $ ✉♥❞ '✳ ❉❛  ❧✐♥❡❛r ✈♦♥  ❛❜❤ä♥❣t✱ ❢♦❧❣t ✉♥t❡r ❆✉s♥✉t③✉♥❣ ❞❡r ❊✐❣❡♥s❝❤❛❢t❡♥ ❞❡s ❊r✇❛rt✉♥❣s✇❡rt❡s ❢ür ❞❡♥ ❊r✇❛rt✉♥❣s✇❡rt ✈♦♥  ✿    '  &   '  &    ' ✶✳✶✷✳ ❇▲❆❈❑✲❙❈❍❖▲❊❙✲▼❖❉❊▲▲ ❋Ü❘ ❆❑❚■❊◆❑❯❘❙P❘❖❩❊❙❙❊ ✸✸ ❆♥❛❧♦❣ ❧ässt s✐❝❤ ❞✐❡ ❱❛r✐❛♥③ ✈♦♥  ❜❡st✐♠♠❡♥✳ ❊s ❣✐❧t✿    '  &   &     &  ' ❉❛♠✐t ❢♦❧❣t✱ ❞❛ss ❞✐❡ ❘❡♥❞✐t❡ ♥♦r♠❛❧✈❡rt❡✐❧t ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ ' ✉♥❞ &  ' ✐st✳ ❉❛❜❡✐ s✐♥❞ ❞✐❡ ✐♥ ❑❛♣✐t❡❧ ✶✳✽ ❜❡st✐♠♠t❡♥ st❛t✐st✐s❝❤❡♥ ❑❡♥♥③❛❤❧❡♥  ✉♥❞ % ❙❝❤ät③✲ ✇❡rt❡ ❢ür ✉♥s❡r❡ ▼♦❞❡❧❧♣❛r❛♠❡t❡r  ✉♥❞ & ✐♠ ❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦❞❡❧❧✳ ❇❡✐ ❜❡❦❛♥♥t❡♠ ❆❦t✐❡♥❦✉rs  ③✉r ❩❡✐t '  $ ✉♥❞ ♠✐t ❞❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐ts❛✉ss❛❣❡♥ ③✉  s✐♥❞ ü❜❡r ❞❡♥ ❩✉s❛♠♠❡♥❤❛♥❣     ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐ts❛✉ss❛❣❡♥ ü❜❡r ❞❡♥ ❑✉rs ③✉r ❩❡✐t '  $ ♠ö❣❧✐❝❤✿    ✳ ❇❡✐s♣✐❡❧ ✶✳✶✷✳✷ ✭▼♦❞❡❧❧✐❡r✉♥❣ ❡✐♥❡s ❆❦t✐❡♥❦✉rs❡s ♠✐tt❡❧s ❞❡s ❇❧❛❝❦✲❙❝❤♦❧❡s✲▼♦✲ ❞❡❧❧s✮✳ ❲✐r ❜❡tr❛❝❤t❡♥ ❡r♥❡✉t ❞✐❡ ❆❞✐❞❛s✲❆❦t✐❡ ❛✉s ❇❡✐s♣✐❡❧ ✶✳✽✳✹✳ ❉❡r ▼✐tt❡❧✇❡rt ❞❡r ✈❡r❣❛♥❣❡♥❡♥ ❧♦❣❛r✐t❤♠✐s❝❤❡♥ ❲♦❝❤❡♥r❡♥❞✐t❡♥ ❜❡tr✉❣ ✵✱✵✵✹✾✱ ❞✐❡ ❙t❛♥❞❛r❞❛❜✇❡✐✲ ❝❤✉♥❣ ✵✱✵✷✹✻✳ ❆♠ ✶✾✳✵✺✳✵✽ ❧❛❣ ❞❡r ❆❦t✐❡♥❦✉rs ❜❡✐ ✹✺✱✾✺✳ ❊s s♦❧❧ ❞✐❡ ❲❛❤rs❝❤❡✐♥✲ ❧✐❝❤❦❡✐t ❞❛❢ür ❜❡st✐♠♠t ✇❡r❞❡♥✱ ❞❛ss ❞❡r ❆❦t✐❡♥❦✉rs ❞r❡✐ ❲♦❝❤❡♥ s♣ät❡r ✹✼✱✵✵ ü❜❡r✲ st❡✐❣t✳ ●❡♠äÿ ✉♥s❡r❡r ▼♦❞❡❧❧❛♥♥❛❤♠❡ ❣✐❧t   !

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Mathematics and the search for knowledge [...] XA-GB by Morris Kline


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