Elementary Synthetic GeometryJ. Wiley & sons, 1896 - 164 Seiten |
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Seite 145
... every one is the orthocenter of the other 3 . 12. A , B , C and their orthocenter H are the centers of the 4 os which touch DEF , the orthocentric A. BOOK VIII . RECENT GEOMETRY . [ The Lemoine - EXERCISES ON BOOK VII . 145.
... every one is the orthocenter of the other 3 . 12. A , B , C and their orthocenter H are the centers of the 4 os which touch DEF , the orthocentric A. BOOK VIII . RECENT GEOMETRY . [ The Lemoine - EXERCISES ON BOOK VII . 145.
Seite 146
George Bruce Halsted. BOOK VIII . RECENT GEOMETRY . [ The Lemoine - Brocard Geometry . ] CHAPTER I. ANTI - PARALLELS , ISOGONALS , SYMMEDIANS . 624. Two mutually equiangular polygons are co - sensal when rays pivoted within them and ...
George Bruce Halsted. BOOK VIII . RECENT GEOMETRY . [ The Lemoine - Brocard Geometry . ] CHAPTER I. ANTI - PARALLELS , ISOGONALS , SYMMEDIANS . 624. Two mutually equiangular polygons are co - sensal when rays pivoted within them and ...
Seite 149
... Lemoine p't , meet the sides , is called the 2d Lemoine O of that A. 645. Since the sides of a △ and of its orthocentric △ are anti- , .. the sides of the orthocentric are bisected by the symmedians . .. join each angle of a △ to the ...
... Lemoine p't , meet the sides , is called the 2d Lemoine O of that A. 645. Since the sides of a △ and of its orthocentric △ are anti- , .. the sides of the orthocentric are bisected by the symmedians . .. join each angle of a △ to the ...
Seite 150
... Lemoine point of a triangle is the center of perspective of that triangle and its polar triangle with respect to any circle . Proof . With respect to circum - O of A ABC , the pole of BC is P , of CA is Q , of AB is R. LPM || to QR is ...
... Lemoine point of a triangle is the center of perspective of that triangle and its polar triangle with respect to any circle . Proof . With respect to circum - O of A ABC , the pole of BC is P , of CA is Q , of AB is R. LPM || to QR is ...
Seite 151
... Lemoine p't ] , to AB , BC , CA. .. K is the mid p't of these sects and aßß'y ' is a rect ' . The median BB ' [ of △ ABC ] cuts ay ' in its mid p't M ; and if MK meets AC in N , KM KN ; and MKN is to aß , and .. to BE , the alt ' from ...
... Lemoine p't ] , to AB , BC , CA. .. K is the mid p't of these sects and aßß'y ' is a rect ' . The median BB ' [ of △ ABC ] cuts ay ' in its mid p't M ; and if MK meets AC in N , KM KN ; and MKN is to aß , and .. to BE , the alt ' from ...
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altitude angle equal angle-bisector angles opposite axis of symmetry bisects Brocard p't called cenquad circumcenter co-straight coincide common point concurrent concyclic congruent Construction Corollary corresponding diagonal diameter draw end point Engineering equal angles equal sects equal sides equiangular polygon explemental exterior angle figure g-line Geometry given p't given point given straight greater harmonic conjugates harmonic range inscribed inscribed angles intercept intersection point inversely isogonal isogonal conjugates Lemoine p't Lemoine point lune magnitude median mid p't mid point morocco opposite sides orthocenter parallel parallelogram pencil perigon perspective plane polar pole polygon Proof quad quadrant quadrilateral radius rectangle rhombus right angles rotation sect joining semicircle sides equal sphere spherical angle spherical polygon spherical triangle square st's straight angle supplemental symcenter symcentral symmedians symmetrical with regard symtra tangent Theorem third side transversal vertex vertices
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