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Philippe de La Hire (or Lahire, La Hyre or Phillipe de La Hire) (18 March 1640 – 21 April 1718) was a French painter, mathematician, astronomer, and architect. According to Bernard le Bovier de Fontenelle he was an "academy unto himself".
La Hire set off for Venice in 1660 and there spent four years developing his artistic skills and learning geometry. The interest in geometry arose from his study of perspective in art, but soon he was finding his mathematics classes more enjoyable than painting.
Dec 24, 2016 · Philippe de la Hire was a mathematician, an observational astronomer, and a key figure in the Académie royale des sciences. La Hire was the eldest child of Laurent de la Hire, peintre ordinaire du roi and professor at the Académie royale de peinture, and Marguerite Coquin.
- dj.sturdy@ulst.ac.uk
- La Hire
- Theorem 1
- Proof
- Theorem 2
- Desargues
- Definition
- Lemma 1
- Theorem 3
We have already noted the pole — polar pairing of a point and a line, with respect to a given conic section, as found in the Conicsof Apollonius. Both Desargues and La Hire approached the topic projectively, by handling the topic for a circle and then showing that the relation found for the base circle was preserved in projection to the conic secti...
Suppose H(AC, BD) on line AD and AD is projected from a point E onto line AH that is parallel to ED, B to G and C to H. Then G is the midpoint of AH.
See Fig. 2Center Left. By similar triangles, Solving for DEin each equation gives The numerator is (CB + CD)(AB + CB) = AB ⋅CD + CB(AB + BC + CD) = AB ⋅CD + CB ⋅AD so division by AB ⋅ CD = AD ⋅ CB shows that AH ÷ AG= 2. Lemma 7 follows, the claim that when two lines meet at B so H(BG, FH) and H(BD, CE) for points on those lines, then the lines on c...
Given a circle, let x be the polar of X and y the polar of Y . Then Y is on x exactly when X is on y. (Note that cases when X or Yis on the circle or at the center of the circle were not considered.) What about the conic sections? The Pole-Polar Theoremapplies just as well to the conic sections: “all that follows is a simple application of these le...
How did Desargues handle that material? For him, the key figure was a quadrilateral inscribed in a conic, and he began with the relation that he called involution, on collinear points.
Collinear pairs L, M; I, K; H, G are points in involution when there is a collinear point Q — called the souche — so QL ⋅ QM = QI ⋅ QK = QH ⋅ QG, with Qseparating either all or none of the pairs. In Fig. 4 Right, for example, pairs P, Q; L, M; H, G; I, K are in involution, where the souche would be between Q and L. Desargues characterized in the fo...
Let B, H; C, G; D, F be three pairs in involution with souche A. Then This is the same as CR(GC, BD) =CR(GC, HF) in absolute value, where CR(XY, WZ) denotes \(\frac {XW \cdot YZ}{XZ \cdot YW}\). [Corresponding equations hold for the other pairs.]
Let BCDE be inscribed in a conic, where BE meets CD at F. Let a line meet the conic at L and M, meet CD at Q, BE at P, CB at I, ED at K, BD at G, and CE at H. Then pairs Q, P; L, M; I, K; H, G are points in involution. [See Figure 4 Right.] (Field and Gray1987, p. 108).
- Christopher Baltus
- christopher.baltus@oswego.edu
- 2020
Philippe de La Hire was born in Paris in 1640. As the eldest son, he received drawing and painting lessons from his father Laurent de la Hyre [1] (1606-1656), who saw him as his successor. Indeed, Laurent de la Hyre was a well-known artist, a member of the Royal Academy of Painting and Sculpture; painters, engravers and mathematicians attended ...
Mar 18, 2020 · During his career, Philippe de La Hire contributed to many fields of science, even though he always preferred geometry. He published a comprehensive work on conic sections which contained a description of Desargues’ projective geometry in 1685 .
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Philippe de La Hire (or Lahire, La Hyre or Phillipe de La Hire) (18 March 1640 – 21 April 1718) was a French painter, mathematician, astronomer, and architect. According to Bernard le Bovier de Fontenelle he was an "academy unto himself".
