XYIII. MENSURATION : HERON OF ALEXANDRIA, pages 298-354 
Geodaesia, 
Controversies as to Heron’s date . 
Character of works .... 
List of treatises 
Geometry 
(a) Commentary on Euclid’s Elements 
(/3) The Definitions .... 
Mensuration 
The Metrica, Geometrica, Stereometrica, 
Mensurae ..... 
Contents of the Metrica 
Book I. Measurement of areas 
(a) Area of scalene triangle 
Proof of formula A = {s(s — «) (s — h (s — c)} 
(/3) Method of approximating to the square root 
of a non-square number 
(•y) Quadrilaterals 
(8) Regular polygons with 8, 4, 5, 6, 7, 8, 9,10 
11, or 12 sides 
(f) The circle 
(£) Segment of a circle 
(r/) Ellipse,parabolic segment,surface of cylindei 
right cone, sphere and segment of sphere 
Book II. Measurement of volumes 
(a) Cone, cylinder, parallelepipedi prism), pyramid 
and frustum 
(/3) Wedge-shaped solid (/3co/nVKoy or rr^mncos) 
(y) Frustum of cone, sphere, and segment thereof 
(8) Anchor-ring or tore 
{() The two special solids of Archimedes VMethoc 
(£) The five regular solids . 
Book III. Divisions of figures 
Approximation to the cube root of a noi 
number 
Quadratic equations solved in Heron . 
Indeterminate problems in the Geometrica 
The Dioptra 
The Mechanics .... 
Aristotle’s Wheel . 
The parallelogram of velocities 
Motion on an inclined plane . 
On the centre of gravity 
The five mechanical powers . 
Mechanics in daily life : queries and answers 
Problems on the centre of gravity, &c. . 
The Catoptrica 
Heron’s proof of equality of angles of incidence and 
reflection 
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307- 308 
308- 310 
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314-316 
316-344 
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320-344 
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320- 321 
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331 
331- 335 
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