From the Abacus To the iphone

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1 From the Abacus To the iphone 3 CMC South Spring Conference 2017 John Martin Santa Rosa Junior College

2 From the Abacus To the iphone ENIAC Abacus iphone 1 HP-35

3 The Main Characters Wilhelm Schickard Blaise Pascal Gottfried Wilhelm Leibniz

4 The Calculating Clock Wilhelm Schickard Herrenburg

5 The Calculating Clock Wilhelm Schickard Johannes Kepler What you have done in a logistical way, I have just tried to do by way of mechanics. I have constructed a machine consisting of eleven complete and six incomplete sprocket wheels, which can calculate. You would burst out laughing if you were present to see how it carries by itself from one column of tens to the next or borrows from them during subtraction. Wilhelm Schickard

6 The Calculating Clock Schickard s drawings, 1624

7 The Calculating Clock Computer History Museum Mountain View, California

8 The Calculating Clock Multiplying Unit Six digit, decimal adding machine Storage for Intermediate Results

9 Napier s Rods

10 Example: 423 X 6 Napier s Rods 6 = = 5 = 3 = 8 SET OF RODS 423 X 6 = 2538 BOARD

11 The Calculating Clock Back View Sheet of Paper With 10 Rods

12 The Calculating Clock Input Dials Dials and Wheels Gears

13 Blaise Pascal

Les Machine Arithmétiques de Blaise Pascal Blaise Pascal Pascaline I submit to the public a small machine by my invention, by means of which you alone

14 Les Machine Arithmétiques de Blaise Pascal Blaise Pascal Pascaline I submit to the public a small machine by my invention, by means of which you alone may, without any effort, perform all the operations of arithmetic, and may be relieved of the work which has often times fatigued your spirit. Blaise Pascal

15 The Pascaline Clermont-Ferrand

16 The Pascaline Clermont-Ferrand Musée Henri-Lecoq Clermont-Ferrand, France

17 The Pascaline The Marguerite Périer

18 The Pascaline The Queen of Sweden

19 The Pascaline

20 The Pascaline Input Dial Output Drum

21 The Nines Complement Method Definition: The nines complement of any one digit decimal number d is 9 d. Examples: The nines complement of 3 is 6. The nines complement of 9 is 0. Notation: Let the nines complement of A be denoted by ncp (A).

22 The Nines Complement Method Definition: The nines complement of any one digit decimal number d is 9 d. For any n digit decimal number A, we have: So that: ncp (538) = 10 3 n ncp (A) = 10 1 A = = 461

23 The Nines Complement Method Using: n ncp (A) = 10 1 A We have: ncp (A B) n = 10 1 (A B) n = 10 1 A + B = ncp (A) + B Note: ncp (ncp (#)) = # Thus: A B = ncp (ncp (A) + B)

24 The Nines Complement Method Thus: A B = ncp (ncp (A) + B) Example: Standard Method 9 s Complement Method 538 ncp ncp 525

25 The Pascaline The Scientific Machines

26 The Pascaline The Chancelier Séguier The Accounting Machines all other dials fourth dial third dial second dial first dial base 10 Hundreds base 10 Tens base 10 Livres base 20 base 12 Sols Deniers

27 The Pascaline The Léon Parcé Collection The Surveying Machines all other dials fourth dial third dial second dial first dial base 10 Tens base 10 Toises base 6 Pieds base 12 Pouce base 12 Lignes

28 The Pascaline Musée des Arts et Métiers Paris Musée Henri-Lecoq Clermont-Ferrand Musée Roger Quillot Clermont-Ferrand

29 Gottfried Wilhelm Leibniz The Derivative: The Integral: dy dx f (x) dx

30 Gottfried Wilhelm Leibniz Several years ago I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian. It occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only counting but also addition and subtraction, multiplication and division could be accomplished by a suitably arranged machine easily, promptly, and with sure results. Gottfried Wilhelm Leibniz

31 Gottfried Wilhelm Leibniz Library Hanover, Germany

32 Hanover Hanover

35 Mechanical Calculators of the 17th Century The Stepped Reckoner

36 The Stepped Reckoner Staffelwalze Stepped drum

37 The Stepped Reckoner Output wheel Input dial Rotating rod Stepped drum

38 The Stepped Reckoner Stepped Drum Rod Drive Crank Input Dial

39 The Odyssey of the Younger Machine : Under construction : Stored in Hanover : Stored in Göttingen : Returned to Hanover : Restored 1896 present: Gottfried Wilhelm Leibniz Library

40 Mechanical Calculators of the seventeenth century

Early Aids To Calculation

Early Aids To Calculation Thomas J. Bergin Computer History Museum American University 7/9/2012 1 Quipu 7/9/2012 2 Pebbles -Calculus: n; pl. calculi, calculuses (Latin, calculus, a small stone or pebble