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Date: circa 1856

Inventory Number: 5467

Classification: Demonstration Model

Subject:

Maker: Fabre et Cie

Inventor: Théodore Olivier (1793 - 1853)

Cultural Region:

Place of Origin:

City of Use:

Dimensions:

69.5 × 25 × 28.5 cm (27 3/8 × 9 13/16 × 11 1/4 in.)

DescriptionThe model sits in a square mahogany box with a circular opening on the top panel. Each of the four bottom corners is raised on a small round stand. There is a base board trim around the bottom of the box and the top panel extends slightly forming a lip around the top of the box. There is a brass plaque at the bottom left-hand corner of the top panel. Henceforth the edge on which the plaque is centered will be used as the 'front' of the box, e.g. the 'right side' of the box is on the right of someone facing center. The outer walls of the box can be removed, revealing four, unfinished, table legs.

The model frame is made of thin, rectangular, brass bars. One such bar is attached to each side of the diameter of the circular opening on the top panel of the box that runs parallel to the front edge. These two bars stand vertically. They are connected by shorter, horizontal brass bars in two places. One of the horizontal bars is fixed at the top of the two vertical ones. The bar is fixed on both sides by brass handles, on the outside of the vertical bars. The second horizontal bar is moveable. It too is attached to the vertical bars by a handle on each side, on the outside of the vertical bars, but, when loosened, these handles permit the user to slide the bar up and down in tracks carved out of the vertical bars. Sliding this bar up and down changes the vertical height of the modeled cylinder.

The bottom horizontal bar also acts as the horizontal diameter of a brass circle held in place by the frame. There is a second, perpendicular brass bar running the vertical diameter of the circle. The intersection of the two bars in the center is formed into a flat brass circle with a small hole in the center. When the horizontal bar slides up and down in the tracks on the vertical bars, the circle moves with it. The circle can also pivot forward and backwards, altering the angle between the vertical diameter and the vertical brass bars. All rotational and vertical movement of the disc is possible when the handles are loosened, and they can be tightened again to keep the disc in place.

The top horizontal bar is also attached to a brass circle but it is not itself fixed as a diameter of the circle. On the top and at the center of the top horizontal bar, there is a brass handle, identical to those that attach each horizontal bar to the vertical bars. The handle attachment goes through the horizontal bar and is attached to the center of the brass circle. By loosening the handle, the top circle can rotate around its center and pivot forward and backward like the bottom disc. The circle has two brass bars as perpendicular diameters with a circle in their intersection, identical to the bottom circle.

There are 120 small, equally spaced holes all along the circumference of both circles. Long, thin, golden threads are folded in half with each end going through one of two neighboring holes in the top and bottom circle's circumference. There are 60 threads. There is a vertical, grey, elongated egg-shaped weight tied to the bottom of each end of each thread, pulling them taunt. The weights are concealed within the mahogany box. They can be seen when the outer walls of the box are removed.

The model frame is made of thin, rectangular, brass bars. One such bar is attached to each side of the diameter of the circular opening on the top panel of the box that runs parallel to the front edge. These two bars stand vertically. They are connected by shorter, horizontal brass bars in two places. One of the horizontal bars is fixed at the top of the two vertical ones. The bar is fixed on both sides by brass handles, on the outside of the vertical bars. The second horizontal bar is moveable. It too is attached to the vertical bars by a handle on each side, on the outside of the vertical bars, but, when loosened, these handles permit the user to slide the bar up and down in tracks carved out of the vertical bars. Sliding this bar up and down changes the vertical height of the modeled cylinder.

The bottom horizontal bar also acts as the horizontal diameter of a brass circle held in place by the frame. There is a second, perpendicular brass bar running the vertical diameter of the circle. The intersection of the two bars in the center is formed into a flat brass circle with a small hole in the center. When the horizontal bar slides up and down in the tracks on the vertical bars, the circle moves with it. The circle can also pivot forward and backwards, altering the angle between the vertical diameter and the vertical brass bars. All rotational and vertical movement of the disc is possible when the handles are loosened, and they can be tightened again to keep the disc in place.

The top horizontal bar is also attached to a brass circle but it is not itself fixed as a diameter of the circle. On the top and at the center of the top horizontal bar, there is a brass handle, identical to those that attach each horizontal bar to the vertical bars. The handle attachment goes through the horizontal bar and is attached to the center of the brass circle. By loosening the handle, the top circle can rotate around its center and pivot forward and backward like the bottom disc. The circle has two brass bars as perpendicular diameters with a circle in their intersection, identical to the bottom circle.

There are 120 small, equally spaced holes all along the circumference of both circles. Long, thin, golden threads are folded in half with each end going through one of two neighboring holes in the top and bottom circle's circumference. There are 60 threads. There is a vertical, grey, elongated egg-shaped weight tied to the bottom of each end of each thread, pulling them taunt. The weights are concealed within the mahogany box. They can be seen when the outer walls of the box are removed.

Signedengraved on a plaque in the bottom lefthand corner of wooden base: INV(T) TH. OLIVIER, 1830 / Fec(t) FABRE ET C(IE) SUCC(R) DE PIXII, / Paris

[all items in parentheses are superscript font in the engraving]

[all items in parentheses are superscript font in the engraving]

FunctionThéodore Olivier designed these string models as pedagogical tools for students and professors of Descriptive Geometry. Descriptive Geometry is the branch of mathematics devoted to the study of three dimensional objects in terms of two dimensional projections or representations of those objects. Of particular interest are the two-dimensional cross-sections of geometric objects, the surfaces of intersection-objects between two three-dimensional objects, the surfaces of three-dimensional objects, and the two-dimensional projections, or shadows, of three dimensional objects. In her article, "The Physicalist Tradition in Early Nineteenth Century French Geometry", Lorraine Daston indicates that Descriptive Geometry was deeply connected to the application-based pedagogical tradition of the newly founded (in 1784) École Polytechnique[1]. As such, physicalist, mechanics-based transformations like 'projection', 'rotation', and 'cross-section' were given geometrical interpretations and the resulting objects studied. In spite of being a rigorous and abstract field of mathematics, Descriptive Geometry was also extremely useful for stone-cutters, engineers, artillery specialists, military personnel, and other technically oriented students of the École.

Descriptive Geometry was developed by Gaspard Monge, a professor and the curriculum director at the École Polytechnique in the late 1700s and early 1800s. He proposed Descriptive (or Synthetic) Geometry as an alternative to the algebraic mathematical paradigm of the 18th century. Monge was in part responding to a general mathematical concern over the lack of rigorous grounding for the calculus. Most attempts to make the calculus rigorous were algebraic. However, there was also a growing concern that algebra was too un-tethered from experience and physical reality and that. According to Daston, part of the anxiety surrounding algebra was a result of the rise in popularity of Lockean empiricism which holds that "all valid knowledge is necessarily rooted in experience".[2] She elaborates as follows:

"The guarantee of a mathematical argument was for them ultimately a psychological one, which depended on the clarity and vivacity of the mental images before the mind's eye of the mathematician. Although this view has an (early) Cartesian ring to it, the emphasis upon "imagination or vision" betrays the influence of Locke in linking the essential clarity and distinctness to perception"[3].

Theodore Olivier studied Descriptive Geometry at the École Polytechnique and went on to be a professor himself at the École Centrale des Arts et Manufacture and a tutor at the École Polytechnique. In the spirit of the École Polytechnique and Monge's mathematical empiricism, Olivier was firmly convinced that in order for students to appreciate the complexities of geometric surfaces, they must be able to 'see' them:

"C'est ainsi que l'on commence à comprendre, que, lorsque l'on veut parler aux élèves des propriétés d'une surface, la première chose à faire est de mettre sous leurs yeux le relief de cette surface, pour qu'ils voient distinctement ce dont on veut leur parler"[4].

As such, he developed his models to enable students of Descriptive Geometry to see the surfaces of geometric objects and to observe the changing patterns of their intersections and certain features of their surfaces.

According to William C. Stone, a mathematics professor at Union College that has repaired and collected many Olivier models, there are 'about' forty-five models in the original set [5]. All but two models in the collection represent the three-dimensional geometric objects by virtue of ruled surfaces. A ruled surface is a surface that can be swept out by the motion of a straight line. The models represent such surfaces by virtue of being constituted by strings pulled taunt between two points to represent straight lines. Each string is like a moment in the line's sweeping path of the object in question. Olivier's string models are like a series of snap shots in the construction of a surface by the motion of a straight line.

According to the "Thirty-Second Annual report of the President of Harvard College" in the academic year of 1856 - 1857, Harvard acquired a complete set of Olivier models in that year for use in mathematics classes. The Report stated the following:

"A complete set of the celebrated models of Olivier has been procured for the use of the mathematical classes. These models, of which there are above fifty, are curiously contrived, by means of moveable parts connected with silken cords, so as to illustrate all the higher researches in Descriptive Geometry, presenting to the eye of the pupil obvious solutions of problems upon complicated surfaces, which might even exhaust the powers of the higher Analytic Geometry. The cost of the collection was about a thousand dollars, the whole amount having been contributed by a few friends of the College, at the instance of Professor Peirce"[6].

Only four of Harvard's Olivier models survive in the Collection of Scientific Instruments.

This model represents various configurations of a cylinder. Let the vertical axis run between the center of the top and bottom discs. The model permits the user to manipulate three components of the cylinder: the height of the vertical axis, the angle of the strings with the vertical axis and with them, the graduated dilatometers of the circle, and the angle of the top and bottom circles with the vertical axis. In its 'simplest' configuration, the top disc is not rotated: all the strings descend parallel to the vertical axis and the diameter of the cylinder is equal to the diameter of the top and bottom brass discs at every point along the vertical axis. As the top disc is rotated, the angle between the strings and the vertical axis increases and the diameter in the center of the cylinder decreases. Tilting the top and bottom discs and altering the height of the cylinder serve to stretch and contract the surface in various ways, demonstrating to the user how certain operations alter the relative components of a cylinder.

[1] Daston, Lorraine. "The Physicalist Tradition in Early Nineteenth Century French Geometry", in STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE, 17 (1986), pp. 269 - 295.

[2] Daston, p. 271.

[3] Daston, p. 274.

[4] Olivier, Theodore. COURS DE GEOMETRIE DESCRIPTIVE; PREMIERE PARTIE: DU POINT, DE LA DROITE ET DU PLAN. Paris: Carilian-Goeury et Vor Dalmost, Libraire des Corps des Ponts et Chaussées et des Mines, Quai des Augustins, no. 49, 1852, p. x

[5] Stone, William C. "Old Science, new art" in UNION COLLEGE, Volume 75, Number 3, (January-February 1983), pp. 10 - 11.

[6] Walker, James. "Thirty-Second Annual Report of the President of Harvard College to the Overseers, exhibiting the state of the institution for the academic year 1856 - 57", Cambridge: Metcalf and Company, Printers to the University, 1858.

Descriptive Geometry was developed by Gaspard Monge, a professor and the curriculum director at the École Polytechnique in the late 1700s and early 1800s. He proposed Descriptive (or Synthetic) Geometry as an alternative to the algebraic mathematical paradigm of the 18th century. Monge was in part responding to a general mathematical concern over the lack of rigorous grounding for the calculus. Most attempts to make the calculus rigorous were algebraic. However, there was also a growing concern that algebra was too un-tethered from experience and physical reality and that. According to Daston, part of the anxiety surrounding algebra was a result of the rise in popularity of Lockean empiricism which holds that "all valid knowledge is necessarily rooted in experience".[2] She elaborates as follows:

"The guarantee of a mathematical argument was for them ultimately a psychological one, which depended on the clarity and vivacity of the mental images before the mind's eye of the mathematician. Although this view has an (early) Cartesian ring to it, the emphasis upon "imagination or vision" betrays the influence of Locke in linking the essential clarity and distinctness to perception"[3].

Theodore Olivier studied Descriptive Geometry at the École Polytechnique and went on to be a professor himself at the École Centrale des Arts et Manufacture and a tutor at the École Polytechnique. In the spirit of the École Polytechnique and Monge's mathematical empiricism, Olivier was firmly convinced that in order for students to appreciate the complexities of geometric surfaces, they must be able to 'see' them:

"C'est ainsi que l'on commence à comprendre, que, lorsque l'on veut parler aux élèves des propriétés d'une surface, la première chose à faire est de mettre sous leurs yeux le relief de cette surface, pour qu'ils voient distinctement ce dont on veut leur parler"[4].

As such, he developed his models to enable students of Descriptive Geometry to see the surfaces of geometric objects and to observe the changing patterns of their intersections and certain features of their surfaces.

According to William C. Stone, a mathematics professor at Union College that has repaired and collected many Olivier models, there are 'about' forty-five models in the original set [5]. All but two models in the collection represent the three-dimensional geometric objects by virtue of ruled surfaces. A ruled surface is a surface that can be swept out by the motion of a straight line. The models represent such surfaces by virtue of being constituted by strings pulled taunt between two points to represent straight lines. Each string is like a moment in the line's sweeping path of the object in question. Olivier's string models are like a series of snap shots in the construction of a surface by the motion of a straight line.

According to the "Thirty-Second Annual report of the President of Harvard College" in the academic year of 1856 - 1857, Harvard acquired a complete set of Olivier models in that year for use in mathematics classes. The Report stated the following:

"A complete set of the celebrated models of Olivier has been procured for the use of the mathematical classes. These models, of which there are above fifty, are curiously contrived, by means of moveable parts connected with silken cords, so as to illustrate all the higher researches in Descriptive Geometry, presenting to the eye of the pupil obvious solutions of problems upon complicated surfaces, which might even exhaust the powers of the higher Analytic Geometry. The cost of the collection was about a thousand dollars, the whole amount having been contributed by a few friends of the College, at the instance of Professor Peirce"[6].

Only four of Harvard's Olivier models survive in the Collection of Scientific Instruments.

This model represents various configurations of a cylinder. Let the vertical axis run between the center of the top and bottom discs. The model permits the user to manipulate three components of the cylinder: the height of the vertical axis, the angle of the strings with the vertical axis and with them, the graduated dilatometers of the circle, and the angle of the top and bottom circles with the vertical axis. In its 'simplest' configuration, the top disc is not rotated: all the strings descend parallel to the vertical axis and the diameter of the cylinder is equal to the diameter of the top and bottom brass discs at every point along the vertical axis. As the top disc is rotated, the angle between the strings and the vertical axis increases and the diameter in the center of the cylinder decreases. Tilting the top and bottom discs and altering the height of the cylinder serve to stretch and contract the surface in various ways, demonstrating to the user how certain operations alter the relative components of a cylinder.

[1] Daston, Lorraine. "The Physicalist Tradition in Early Nineteenth Century French Geometry", in STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE, 17 (1986), pp. 269 - 295.

[2] Daston, p. 271.

[3] Daston, p. 274.

[4] Olivier, Theodore. COURS DE GEOMETRIE DESCRIPTIVE; PREMIERE PARTIE: DU POINT, DE LA DROITE ET DU PLAN. Paris: Carilian-Goeury et Vor Dalmost, Libraire des Corps des Ponts et Chaussées et des Mines, Quai des Augustins, no. 49, 1852, p. x

[5] Stone, William C. "Old Science, new art" in UNION COLLEGE, Volume 75, Number 3, (January-February 1983), pp. 10 - 11.

[6] Walker, James. "Thirty-Second Annual Report of the President of Harvard College to the Overseers, exhibiting the state of the institution for the academic year 1856 - 57", Cambridge: Metcalf and Company, Printers to the University, 1858.

Historical AttributesAccording to the 32nd Annual Report of the President of Harvard College, in 1856 - 1857, this model is one of "above fifty" purchased for the pedagogical use of the Mathematics Department at Harvard University. The collection cost about $1,000.

Curatorial RemarksCuratorial analysis and history of damages and repairs to the Cylinder String Figure in the hand of Ebenezer Gay (formerly assistant curator at the Harvard University Collection of Scientific Instruments), in object file.

Letter from William J.H. Andrewes, curator at the Harvard University Collection of Scientific Instruments, to Garrett Birkhoff, Professor Emeritus in the Harvard Mathematics Department (dated March 23, 1993) inquiring (at the recommendation of I. Bernhard Cohen) if there are any Olivier geometrical string models in existence in the Mathematics department, in object file.

"The Serene Grace of Union College's Geometry Models" article in*THE CHRONICLE OF HIGHER EDUCATION*, dated January 13, 1988, original and photocopy in the instrument file.

A copy of the "Annual Report of the President of Harvard College to the Overseers exhibiting the State of the Institution for the Academic Year 1856 - 57" (Cambridge: Metcalf and Company, printers to the university, 1858) in which the procurement of the models to the mathematics department is heralded, in the object file.

An original copy of the journal UNION COLLEGE for January-February 1983, Volume 75, No. 3, the front and back covers display photos of Olivier demonstration models and an article on pp. 10 - 12 describes and explains the models; the journal was a gift of Mr. Richard Laud in 1983, in the instrument file.

Photocopy of the*COURS DE GEOMETRIE DESCRIPTIVE; Premiere Partie. Du point, le la droite, et du plan*, Deuxieme Edition. Par M. Théodore Olivier (Paris: Carilian-Goeury et V. Dalmont, 1852) in which the inventor describes the models, in object file.

Photocopy of*HISTOIRE DE l'ECOLE CENTRALE DES ARTS ET MANUFACTURES DEPUIS SA FONDATION JUSQU'A CE JOUR*, par Ch. De. Comberousse (Paris: Gauthier-Villars, Imprimeur-Libraire, Bureau des Longitude de L'Ecole Polytechnique, 1879) in which the models are discussed in an Appendix, in instrument file.

Letter from William J.H. Andrewes, curator at the Harvard University Collection of Scientific Instruments, to Garrett Birkhoff, Professor Emeritus in the Harvard Mathematics Department (dated March 23, 1993) inquiring (at the recommendation of I. Bernhard Cohen) if there are any Olivier geometrical string models in existence in the Mathematics department, in object file.

"The Serene Grace of Union College's Geometry Models" article in

A copy of the "Annual Report of the President of Harvard College to the Overseers exhibiting the State of the Institution for the Academic Year 1856 - 57" (Cambridge: Metcalf and Company, printers to the university, 1858) in which the procurement of the models to the mathematics department is heralded, in the object file.

An original copy of the journal UNION COLLEGE for January-February 1983, Volume 75, No. 3, the front and back covers display photos of Olivier demonstration models and an article on pp. 10 - 12 describes and explains the models; the journal was a gift of Mr. Richard Laud in 1983, in the instrument file.

Photocopy of the

Photocopy of

Primary SourcesComberousse, Ch. de. *Histoire de L'Ecole Centrale des Arts et Manufactures, Depuis sa Fondation jusqu'a ce Jour*. Paris: Gauthier-Villars, Imprimeur-Libraire du Bureau des Longitudes, de l'Ecole Polytechnique, Quai des Augustins, no. 55, 1879.

Olivier, Theodore.*Cours de Géométrie Descriptive; Première Partie: Du Point, de la Droite, et du Plan.* Paris: Carilian-Goeury et Vor Dalmost, Libraire des Corps des Ponts et Chaussées et des Mines, Quai des Augustins, no. 49, 1852.

Walker, James. "Thirty-Second Annual Report of the President of Harvard College to the Overseers, exhibiting the state of the institution for the academic year 1856 - 57", Cambridge: Metcalf and Company, Printers to the University, 1858.

Olivier, Theodore.

Walker, James. "Thirty-Second Annual Report of the President of Harvard College to the Overseers, exhibiting the state of the institution for the academic year 1856 - 57", Cambridge: Metcalf and Company, Printers to the University, 1858.

ProvenanceFrom the School of Engineering, attic of Pierce Hall, Harvard University, May 1961.

Related WorksBelhoste, Bruno. "The Ecole Polytechnique and Mathematics in Nineteenth Century France" in *Changing Images in Mathematics: From the French Revolution to the New Millenium*, ed. Umberto Bottazini, Amy Dahan Dalmedico (2001).

Brenni, Paolo. "Dumotiez and Pixii: The Transofrmation of French Philosophical Instruments" in*Bulletin of the Scientific Instrument Society*, (2006), pp. 10 - 16.

Daston, Lorraine. "The Physicalist Tradition in Early Nineteenth Century French Geometry", in*Studies in the History and Philosophy of Science* 17 (1986), pp. 269 - 295.

Shell-Gellasch, Amy. "The Olivier String Models at West Point" in*Rittenhouse* Vol. 17 (2003), pp. 71 - 84.

Brenni, Paolo. "Dumotiez and Pixii: The Transofrmation of French Philosophical Instruments" in

Daston, Lorraine. "The Physicalist Tradition in Early Nineteenth Century French Geometry", in

Shell-Gellasch, Amy. "The Olivier String Models at West Point" in

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