Synthetic geometry

Synthetic geometry is the branch of geometry Geometry

Geometry arose as the field of knowledge dealing with spatial relationships.... 

 which makes use of theorems and synthetic observations to draw conclusions, as opposed to analytic geometry which uses algebra Algebra

Algebra is a branch of mathematics [i] concerning the study of structure [i], relation [i] ... 

 to perform geometric computations and solve problems. The geometry of Euclid Euclid

Euclid , a Greek [i] mathematician [i], who lived in Alexandria [i], Hellenistic Egypt [i], alm ... 

 was indeed synthetic, though not all of the books covered topics of pure geometry.

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Synthetic geometry is the branch of geometry Geometry

Geometry arose as the field of knowledge dealing with spatial relationships.... 

 which makes use of theorems and synthetic observations to draw conclusions, as opposed to analytic geometry which uses algebra Algebra

Algebra is a branch of mathematics [i] concerning the study of structure [i], relation [i] ... 

 to perform geometric computations and solve problems.
The geometry of Euclid Euclid

Euclid , a Greek [i] mathematician [i], who lived in Alexandria [i], Hellenistic Egypt [i], alm ... 

 was indeed synthetic, though not all of the books covered topics of pure geometry.

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