L Bednarz (23 results)

- Softcover
Seller: Doucet, Libraire/Bookseller, L'Assomption, QC, CanadaDoucet, Libraire/Bookseller
Contact seller5-star sellerCondition: Used - Fine
US$ 18.12
US$ 14.00 shippingShips from Canada to U.S.A.Quantity: 1 available
Soft cover. Condition: Fine. No Jacket. Les Publications du Québec, 2013. ix-215 p., illustrations. Couvertures souples. Excellente condition. 9782551252367.

Explore Texas, Texas Edition, Teacherôs Book, Level 4.
Sarah Bednarz, Catherine Clinton, Patricia L.Marshall And Pat Nickell
Published by Houghton Mifflin Harcourt Publishing Company, 1997
- Softcover
Seller: Hawking Books, Edgewood, TX, U.S.A.Hawking Books
Contact seller4-star sellerCondition: Used - Very good
US$ 39.80
Free ShippingShips within U.S.A.Quantity: 1 available
Condition: Very Good. Very Good Condition. Five star seller - Buy with confidence.

- Hardcover
Seller: Antiquariat Renner OHG, Albstadt, GermanyAntiquariat Renner OHG
Contact seller5-star sellerAssociation member: BOEV
Condition: Used - As new
US$ 70.57
US$ 51.39 shippingShips from Germany to U.S.A.Quantity: 1 available
Hardcover. Condition: Wie neu. Dordrecht, Kluwer (1996). gr.8°. Some figs. XV, 345 p. Hardbound. Mathematics Education Library, volume 18.- Incl. bibliography.

- Hardcover
Seller: books4less (Versandantiquariat Petra Gros GmbH & Co. KG), Welling, Germanybooks4less (Versandantiquariat Petra Gros GmbH & Co. KG)
Contact seller5-star sellerCondition: Used - Very good
US$ 176.43
US$ 18.21 shippingShips from Germany to U.S.A.Quantity: 1 available
gebundene Ausgabe. Condition: Gut. 345 Seiten; Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.); Schnitt und Einband sind etwas staubschmutzig; der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend… gut. Text in ENGLISCHER Sprache! Sprache: Englisch Gewicht in Gramm: 800.

- Softcover
Seller: Phatpocket Limited, Waltham Abbey, HERTS, United KingdomPhatpocket Limited
Contact seller5-star sellerCondition: Used - Good
US$ 205.33
US$ 14.10 shippingShips from United Kingdom to U.S.A.Quantity: 1 available
Condition: Good. Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions.

- Softcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
Contact seller5-star sellerCondition: New
US$ 203.97
US$ 16.57 shippingShips from United Kingdom to U.S.A.Quantity: 1 available
Paperback. Condition: Brand New. 1st edition. 368 pages. 9.50x6.25x1.00 inches. In Stock.

- Hardcover
Seller: Phatpocket Limited, Waltham Abbey, HERTS, United KingdomPhatpocket Limited
Contact seller5-star sellerCondition: Used - Good
US$ 287.96
US$ 14.10 shippingShips from United Kingdom to U.S.A.Quantity: 2 available
Condition: Good. Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions.

- Hardcover
Seller: Ria Christie Collections, Uxbridge, United KingdomRia Christie Collections
Contact seller5-star sellerCondition: New
US$ 355.92
US$ 15.88 shippingShips from United Kingdom to U.S.A.Quantity: Over 20 available
Condition: New. In.

- Softcover
Seller: Buchpark, Trebbin, GermanyBuchpark
Contact seller5-star sellerCondition: Used - Fine
US$ 250.12
US$ 119.91 shippingShips from Germany to U.S.A.Quantity: 1 available
Condition: Sehr gut. Zustand: Sehr gut | Seiten: 368 | Sprache: Englisch | Produktart: Bücher | In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated,… except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

- Softcover
Seller: preigu, Osnabrück, Germanypreigu
Contact seller5-star sellerCondition: New
US$ 326.58
US$ 79.94 shippingShips from Germany to U.S.A.Quantity: 5 available
Taschenbuch. Condition: Neu. Approaches to Algebra | Perspectives for Research and Teaching | N. Bednarz (u. a.) | Taschenbuch | Mathematics Education Library | xvi | Englisch | 1996 | Springer | EAN 9780792341680 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann…[at]springer[dot]com | Anbieter: preigu.

Approaches to Algebra
. Ed(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada)
- Hardcover
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, IrelandKennys Bookshop and Art Galleries Ltd.
Contact seller5-star sellerCondition: New
US$ 446.02
US$ 11.99 shippingShips from Ireland to U.S.A.Quantity: 15 available
Condition: New. Aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. This book provides an introduction to generalization, problem solving, modeling, and functions. Edi…tor(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada). Series: Mathematics Education Library. Num Pages: 364 pages, biography. BIC Classification: JNU; PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 155 x 22. Weight in Grams: 698. . 1996. Hardback. . . . .

Language: English
Published by Springer Netherlands, Springer Netherlands, 1996
- Softcover
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
Contact seller5-star sellerCondition: New
US$ 390.34
US$ 71.88 shippingShips from Germany to U.S.A.Quantity: 1 available
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if tho…se magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

Language: English
Published by Springer Netherlands, Springer Netherlands, 1996
- Hardcover
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
Contact seller5-star sellerCondition: New
US$ 390.34
US$ 72.65 shippingShips from Germany to U.S.A.Quantity: 1 available
Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magn…itudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

- Softcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
Contact seller5-star sellerCondition: New
US$ 468.93
US$ 16.57 shippingShips from United Kingdom to U.S.A.Quantity: 1 available
Paperback. Condition: Brand New. 1st edition. 368 pages. 9.50x6.25x1.00 inches. In Stock.

Approaches to Algebra
. Ed(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada)
- Hardcover
Seller: Kennys Bookstore, Olney, MD, U.S.A.Kennys Bookstore
Contact seller5-star sellerCondition: New
US$ 534.24
US$ 10.50 shippingShips within U.S.A.Quantity: 15 available
Condition: New. Aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. This book provides an introduction to generalization, problem solving, modeling, and functions. Edi…tor(s): Bednarz, Nadine; Kieran, Carolyn (Universite du Quebec a Montreal, Canada); Lee, L. (Universite de Quebec a Montreal, Canada). Series: Mathematics Education Library. Num Pages: 364 pages, biography. BIC Classification: JNU; PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 235 x 155 x 22. Weight in Grams: 698. . 1996. Hardback. . . . . Books ship from the US and Ireland.
JOURNAL of PALLIATIVE MEDICINE, Volume 9, Number 4, August 2006, Pages 833 to 1034. Pediatric Palliative Care Moving Forward: Empathy, Competence, Quality, and the Need for Systematic Change; Cost and Utilization Outcomes of Patients Receiving Hospital-Based Palliative Care Consultation; Redefining Cancer-Related Asthenia-Fatigue Syndrome; Survival, Mortality, and Location for Death For Patients Seen by a Hospital-Based Palliative Care Team; Peer-Professional Workgroups in Palliative Care: A Strategy for Advancing Professional Discourse and Practice; Evaluation of an Educational Intervention to Encourage Advance Directive Discussions between Medicine Residents and Patients; A Day in the Life of a Hospice Physician; Palliative Care Case Repo
J. R. CANE; J. D. PENROD; P. DEB; C. LUHRS; C. DELLENBAUGH; C. W. ZHU; T. HOCHMAN; M. L. MACIEJEWSKI; E. GRANIERRI; R. S. MORRISON. S. J. SCIALLA; R. P. COLE; L. BEDNARZ; E. K. FROMME; P. B. BASCOM; M. D. SIMTH; S. W. TOLLE; L HANSON; D. H. HICKM; M. L. OSBORNE; I BYOCK; J. SHEILS TWOHIG; M. MERRIMAN; K. COLLINS; C. DAVIS FURMAN; B. HEAD; B. LAZOR; B. CASPER; C. SEEL RITCHIE; W. G. PORTER; E. PROMER.
Published by Official Journal of the American Academy of Hospice and Palliative Medicine. Mary Ann Liebert, Inc. Publications, * * * * *, 2006
- Softcover
Seller: L. Michael, North Hollywood, CA, U.S.A.L. Michael
Contact seller4-star sellerCondition: Used - Near fine
US$ 65.80
US$ 15.26 shippingShips within U.S.A.Quantity: 1 available
Soft cover. Condition: Near Fine. B00K: Near Fine/, $120.14. Reduced From. JOURNAL of PALLIATIVE MEDICINE, Volume 9, Number 4, August 2006, Pages 833 to 1034. Pediatric Palliative Care Moving Forward: Empathy, Competence, Quality, and the Need for Systematic Change; Cost and Utilization Outcomes of Patients Receiving Hospital-Ba…sed Palliative Care Consultation; Redefining Cancer-Related Asthenia-Fatigue Syndrome; Survival, Mortality, and Location for Death For Patients Seen by a Hospital-Based Palliative Care Team; Peer-Professional Workgroups in Palliative Care: A Strategy for Advancing Professional Discourse and Practice; Evaluation of an Educational Intervention to Encourage Advance Directive Discussions between Medicine Residents and Patients; A Day in the Life of a Hospice Physician; Palliative Care Case Report: Leptomeningeal Carcinomatosis; J. R. CANE; J. D. PENROD; P. DEB; C. LUHRS; C. DELLENBAUGH; C. W. ZHU; T. HOCHMAN; M. L. MACIEJEWSKI; E. GRANIERRI; R. S. MORRISON. S. J. SCIALLA; R. P. COLE; L. BEDNARZ; E. K. FROMME; P. B. BASCOM; M. D. SIMTH; S. W. TOLLE; L HANSON; D. H. HICKM; M. L. OSBORNE; I BYOCK; J. SHEILS TWOHIG; M. MERRIMAN; K. COLLINS; C. DAVIS FURMAN; B. HEAD; B. LAZOR; B. CASPER; C. SEEL RITCHIE; W. G. PORTER; E. PROMER. Official Journal of the American Academy of Hospice and Palliative Medicine. Mary Ann Liebert, Inc. Publications 2006 Tall Wide S/c. Blue Spine With Title In Off-White Letters, Soft Cover Book: Near Fine/, Shelf, Edge, And Corner Wear. Pages 833 to 1034. Printed On Off-White Paper, In Fine/ Condition, Lightly Viewed, Clean, And Tight To The Spine. D/j: None. Description Applies To This B0K, Only, Which Is Hard To Find, And Will Be = Packaged And Shipped Carefully, To Avoid Shipping Damage And Will Make It, An Excellent Addition To Your Own Personal Library Collection, Or As A Gift For The Collector / Reader. WORLD WIDE SHIPPING, AVAILABLE. Volume 9, Number 4, August 2006 B00K: Near Fine/, (illustrator).

- Hardcover
- Print on Demand
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
Contact seller5-star sellerCondition: New
US$ 245.36
US$ 26.27 shippingShips from Germany to U.S.A.Quantity: 2 available
Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, exce…pt if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano. 372 pp. Englisch.

- Softcover
- Print on Demand
Seller: moluna, Greven, Germanymoluna
Contact seller5-star sellerCondition: New
US$ 315.07
US$ 55.94 shippingShips from Germany to U.S.A.Quantity: Over 20 available
Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes…cannot be actually numerically calculated, except if those magnit.

- Hardcover
- Print on Demand
Seller: moluna, Greven, Germanymoluna
Contact seller5-star sellerCondition: New
US$ 315.07
US$ 55.94 shippingShips from Germany to U.S.A.Quantity: Over 20 available
Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actua…lly numerically calculated, except if those magnit.

Language: English
Published by Springer Netherlands, Springer Netherlands Jun 1996, 1996
- Softcover
- Print on Demand
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
Contact seller5-star sellerCondition: New
US$ 377.56
US$ 26.27 shippingShips from Germany to U.S.A.Quantity: 2 available
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculate…d, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano. 368 pp. Englisch.

- Hardcover
- Print on Demand
Seller: preigu, Osnabrück, Germanypreigu
Contact seller5-star sellerCondition: New
US$ 326.58
US$ 79.94 shippingShips from Germany to U.S.A.Quantity: 5 available
Buch. Condition: Neu. Approaches to Algebra | Perspectives for Research and Teaching | N. Bednarz (u. a.) | Buch | xvi | Englisch | 1996 | Springer Netherland | EAN 9780792341451 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: pr…eigu Print on Demand.

Language: English
Published by Springer Netherlands, Springer Netherlands Jun 1996, 1996
- Softcover
- Print on Demand
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germanybuchversandmimpf2000
Contact seller5-star sellerCondition: New
US$ 377.56
US$ 68.52 shippingShips from Germany to U.S.A.Quantity: 1 available
Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, e…xcept if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.

Language: English
Published by Springer Netherlands, Springer Netherlands Jun 1996, 1996
- Hardcover
- Print on Demand
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germanybuchversandmimpf2000
Contact seller5-star sellerCondition: New
US$ 377.56
US$ 68.52 shippingShips from Germany to U.S.A.Quantity: 1 available
Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except i…f those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an 'arithmetic' of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 372 pp. Englisch.