## Proceedings of the American Academy of Arts and Sciences, Volumen1 |

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Página 130

For the opposite vertical angles A D B , CDE are

prop . ... 4 ) the triangles A DB , CDE are identical ; so that their bases A B , C E

are

...

For the opposite vertical angles A D B , CDE are

**equal**( Simson ' s Euclid , B . I . ,prop . ... 4 ) the triangles A DB , CDE are identical ; so that their bases A B , C E

are

**equal**, and their angles A B D , E C D are**equal**; also the angle BAD**equals**...

Página 132

as to make the angles DC F , G FH each

the points D and F , D and G , D and B , by right lines ; also through D draw D K ,

at right angles to DG . Since A B = DC , AC = CF , and the angle BAC

as to make the angles DC F , G FH each

**equal**to the angle B AC , and connectthe points D and F , D and G , D and B , by right lines ; also through D draw D K ,

at right angles to DG . Since A B = DC , AC = CF , and the angle BAC

**equals**the ... Página 135

1 , we can find a derived triangle , which we shall represent by the triangle HIK ,

such that the sum of its angles

a ...

1 , we can find a derived triangle , which we shall represent by the triangle HIK ,

such that the sum of its angles

**equals**... At the point I H make the angle HIL ,**equal**to the angle HIK ; also make the right line IL**equal**to the side I K , and drawa ...

Página 142

3 ) , then since the base - angles of the isosceles triangles represented by A B C ,

A B ́C are

the isosceles triangles are

3 ) , then since the base - angles of the isosceles triangles represented by A B C ,

A B ́C are

**equal**, we have , by cor . to prop . 3 , and hence the vertical angles ofthe isosceles triangles are

**equal**; and the same holds true whether the ... Página 143

4 , since the right triangles ACD , ACB have the angle A common , their other

acute B angles A CD and B are

ABC have a common angle , B , their other acute angles BCD and A are

4 , since the right triangles ACD , ACB have the angle A common , their other

acute B angles A CD and B are

**equal**; alD so since the ( right ) triangles BCD ,ABC have a common angle , B , their other acute angles BCD and A are

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Página 188 - The volumes of the memoirs to be exchanged for the transactions of literary and scientific societies, and copies to be given to all the colleges and principal libraries in this country. One part of the remaining copies may be offered for sale ; and the other carefully preserved, to form complete sets of the work, to supply the demand from new institutions.

Página 188 - ... 3. The results obtained from these appropriations to be published: with the memoirs before mentioned, in the volumes of the Smithsonian Contributions to Knowledge.

Página 345 - Map of the Mineral Lands adjacent to Lake Superior, ceded to the United States by the Treaty of 1842 with the Chippewas.

Página 29 - Such is the state of our language,' says Sheridan, a man certainly not prejudiced against his native tongue, ' that the darkest hieroglyphics, or most difficult ciphers that the art of man has hitherto invented, were not better calculated to conceal the sentiments of those...

Página 156 - On three several Hurricanes of the Atlantic, and their Relations to the Northers of Mexico and Central America, with Notices of other Storms.

Página 189 - Solution of experimental problems, such as a new determination of the weight of the earth, of the velocity of electricity and of light; chemical analyses of soils and plants; collection and publication of articles of science, accumulated in the offices of government.

Página 194 - Regents is a sufficient warrant for the prudence and good judgment which will watch over the general interests of the foundation; while the reputation of the Secretary and his assistant, the Librarian, is so well established in their respective departments, as to render any tribute from the committee entirely superfluous. All which is respectfully submitted by the committee. JAKED SPARKS. EDWAED EVERETT, (Chairman.) BENJAMIN PEIBCK. HENRY "W. LONGFELLOW. ABA GRAY. December 4th, 1847.

Página 188 - Each memoir presented to the Institution to be submitted for examination to a commission of persons of reputation for learning in the branch to which the memoir pertains; and to be accepted for publication only in case the report of this commission is favorable.

Página 33 - Etymologies are at present very uncertain; but such as they are, the old books would still preserve them, and etymologists would there find them. Words in the course of time change their meanings, as well as their spelling and pronunciation, and we do not look to etymology for their present meanings. If I should call a man a knave and a villain, he would hardly be satisfied with my telling him, that one of the words originally signified only a lad or servant; and the other an under-ploughman, or...

Página 29 - It is really deplorable,' as Sir William Jones, speaking of our alphabet, says, ' that our first step from total ignorance should be into gross inaccuracy, and that we should begin our education in English with learning to read the five vowels, two of which, as we are taught to pronounce them, are clearly diphthongs.'— Works, 1st ed., Vol.