Elementos de geometria by Alexis-Claude Clairaut
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"Elementos de geometria" by Alexis-Claude Clairaut is a mathematical textbook written in the mid-18th century. It presents elementary geometry through a practical, problem-driven method rooted in land surveying, aiming to make core concepts intuitive before formalizing them. Expect clear constructions, measurements, and proportional reasoning that build from real needs—measuring distances, areas, and angles—toward the standard toolkit of Euclidean geometry. The opening of the treatise introduces the Portuguese translation, a dedication to the
Marquis of Pombal, and an editor’s note justifying the version as a faster, clearer path to basic geometry. In the prologue, Clairaut argues against the dryness of traditional elements and proposes beginning with practical needs—measuring lengths, distances, and fields—and guiding learners by solving problems rather than presenting theorems first. The first lessons define distance via straight lines, introduce perpendiculars and rectangles (including the square), and show how to construct perpendiculars, parallels, midpoints, and rectangles/squares from given sides. It then moves to measuring areas: product of base and height for rectangles, half the product for triangles, and decomposition of irregular figures into triangles; parallelograms and regular polygons follow, with methods to draw and measure them (using apothems and circle subdivisions). Next come similarity and scaling to handle inaccessible terrain, including constructing similar triangles, dividing segments proportionally, and reducing entire plots to workable diagrams. Finally, it standardizes angle measurement in degrees with a semicircular protractor and transfer tool, proves the triangle angle-sum, reviews isosceles/equilaterals, and shows how to inscribe hexagons, dodecagons, and octagons by dividing the circle. (This is an automatically generated summary.)
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About this eBook
| Author | Clairaut, Alexis-Claude, 1713-1765 |
|---|---|
| Translator | Silva, Joaquim Carneiro da, 1727-1818 |
| Title | Elementos de geometria |
| Original Publication | Lisboa: Regia Officina Typografica, 1772. |
| Credits | Rita Farinha, Hendrik Kaiber, Alberto Manuel Brandão Simões and the Online Distributed Proofreading Team at www.pgdp.net (This file was produced from images generously made available by National Library of Portugal (Biblioteca Nacional de Portugal).) |
| Language | Portuguese |
| LoC Class | QA: Science: Mathematics |
| Subject | Geometry -- Early works to 1800 |
| Category | Text |
| eBook-No. | 78897 |
| Release Date | Jun 20, 2026 |
| Copyright | Public domain in the USA. |
| Downloads | 739 downloads in the last 30 days. |
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