Moore dealt with casuistry in chapter 1. 4 of his Principia Ethica ; he claimed that " the defects of casuistry are not defects of principle ; no objection can be taken to its aim and object.

From the law of excluded middle, formula ✸ 2. 1 in Principia Mathematica, Whitehead and Russell derive some of the most powerful tools in the logician's argumentation toolkit.

( In Principia Mathematica, formulas and propositions are identified by a leading asterisk and two numbers, such as "✸ 2. 1 ".

It is, rather, " one of those innumerable objects of thought which are themselves incapable of definition, because they are the ultimate terms by reference to which whatever is capable of definition must be defined " ( Principia Ethica § 10 ¶ 1 ).

:" It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it so greatly lacking in formal precision in the foundations ( contained in * 1 -* 21 of Principia ) that it represents in this respect a considerable step backwards as compared with Frege.

The solar tidal acceleration at the Earth's surface was first given by Newton in the ' Principia '< ref >, Book 3, Proposition 36, Page 307 Newton put the force to depress the sea at places 90 degrees distant from the Sun at " 1 to 38604600 " ( in terms of g ), and wrote that the force to raise the sea along the Sun-Earth axis is " twice as great ", i. e. 2 to 38604600, which comes to about 0. 52 × 10 < sup >- 7 </ sup > g as expressed in the text .</ ref >

# 1 was issued in July 1987, then reissued in substantially revised form later that year by Rip Off Press ( who had published the original 4th edition of the Principia Discordia in 1970 ).

Surviving preliminary materials show that Newton ( up to some time in 1685 ) conceived his book as a two-volume work: The first volume was to be ' De motu corporum, Liber primus ', with contents that later appeared ( in extended form ) as Book 1 of the ' Principia '.

This had some amendments relative to Newton's manuscript of 1685, mostly to remove cross-references that used obsolete numbering to cite the propositions of an early draft of Book 1 of the Principia.

Bezout's theorem was essentially stated by Isaac Newton in his proof of lemma 28 of volume 1 of his Principia, where he claims that two curves have a number of intersection points given by the product of their degrees.

In his work Principia, he estimated that the ratio of the mass of the Earth to the Sun was about 1 / 28, 700.

He revised his result to obtain a ratio of 1 / 169, 282 in the third edition of the Principia.

The existence of a free nutation of the Earth was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1755 as part of his studies of the dynamics of rotating bodies.

His last work was a revision Andrew Motte's 1729 translation of Newton's Principia, vol. 1 The Motion of Bodies, but he died before it was completed.

Equational logic was common before Principia Mathematica ( e. g., Peirce ,< sup > 1, 2, 3 </ sup > Johnson 1892 ), and has present-day advocates ( Gries and Schneider 1993 ).

In Proposition 66 of Book 1 of the ' Principia ', and its 22 Corollaries, Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions.

In his Principia, Newton proposed the equilibrium shape of a homogeneous rotating Earth was a rotational ellipsoid with a flattening f given by 1 / 230.

( Newton's later first law of motion is to similar effect, Law 1 in the Principia.

This point reappears in Corollaries 1 and 2 to the third law of motion, Law 3 in the Principia.

) This reappears in Book 1, Lemma 10 in the ' Principia '.

) This theorem appears again, with expanded explanation, as Proposition 1, Theorem 1, of the ' Principia '.

This subject reappears in the Principia as Proposition 6 of Book 1.

He can ( 1 ) point his car resolutely at the invading fender and force the other driver back into Lane A ; ;

The Emergency Medical Treatment Unit, Phase 1 ; ;

The estimated standard deviations of the data for two of the resistors were 1 millidegree ; ;

There are hereby created in the Treasury of the United States ( 1 ) a special fund to be known as the Yugoslav Claims Fund ; ;

The 1954 Amendments completely changed the financing of the vocational rehabilitation program, providing for a three-part grant structure -- for ( 1 ) basic support ; ;

With respect to skywave service rendered at night, class 1, -- A stations are the only stations permitted to operate in the United States on clear channels specified for class 1, -- A operation, and so render skywave service free from cochannel interference whereever they may be received ; ;

There are three principal feed bunk types for dairy and beef cattle: ( 1 ) Fence-line bunks -- cattle eat from one side while feed is put in from the opposite side of the fence by self-unloading wagons ; ;

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

Type 1, is represented by the cow, sheep, and pig ; ;

Lobularity is extremely well developed in type 1 ; ;

After passing Af through DEAE-cellulose, the titer of antibodies to WTV in the specific fraction was 1: 4 of the titer before such passage ( precipitin ring tests by R. F. Whitcomb ) ; ;

It has further been shown that: ( 1 ) an experimental neurosis in its initial stages is associated with a reversible shift in the central autonomic balance ; ;

And if the foreigners fighting in the Katanga Army are mercenaries then Lafayette and Von Steuben were mercenaries too, as were also the members of the Lafayette Escadrille in the early part of World War 1, and of Chennault's Flying Tigers in the early days of World War 2.

The reasons are obvious: ( 1 ) the state is buying in quantity, and ( 2 ) it has no federal excise or state sales tax to pay.

Taxation of tangible movable property in Rhode Island has been generally of a `` hands off '' nature due possibly to several reasons: ( 1 ) local assessors, in the main, are not well paid and have inadequate office staffs, ( 2 ) the numerous categories of this component of personal property make locating extremely difficult, and ( 3 ) the inexperience of the majority of assessors in evaluating this type of property.

Among the many problems in the taxing of personal property, and of movable tangible property in particular, two are significant: ( 1 ) situs, ( 2 ) fair and equitable assessment of value.

In order to assist the States in maintaining basic vocational rehabilitation services, Section 2 of the amended Act provides that allotments to States for support of such services be based on ( 1 ) need, as measured by a State's population, and ( 2 ) fiscal capacity, as measured by its per capita income.

This claim, as submitted to the District Court and dismissed by it, 126 F.Supp.235, alleged violation not only of 7 of the Clayton Act, but also of 1 and 2 of the Sherman Act.

He claims that he was denied due process of law in violation of the Fifth Amendment, because ( 1 ) at a hearing before a hearing officer of the Department of Justice, he was not permitted to rebut statements attributed to him by the local board, and ( 2 ) at the trial, he was denied the right to have the hearing officer's report and the original report of the Federal Bureau of Investigation as to his claim.

In the event the total of rupees accruing to the Government of the United States of America as a consequence of sales made pursuant to this Agreement is different from the rupee equivalent of $1,276 million, the amounts available for the purposes specified in paragraph 1, Article 2, will be adjusted proportionately.

I have the honor to refer to the Agricultural Commodities Agreement signed today between the Government of the United States of America and the Government of India ( hereinafter referred to as the Agreement ) and, with regard to the rupees accruing to uses indicated under Article 2, of the Agreement, to state that the understanding of the Government of the United States of America is as follows: 1.

With respect to Article 2,, Paragraph 1 ( A ) of the Agreement: ( 1 )

With respect to Article 2,, paragraphs 1 ( B ) and 1 ( C ): Uses of Section 104 ( E ) and Section 104 ( G ) rupees: The Government of India will use the amount of rupees granted or loaned to it by the United States pursuant to paragraphs 1 ( B ) and 1 ( C ) for projects to promote economic development with emphasis upon the agricultural sector including food reserve storage structures and facilities as may from time to time be agreed upon by the authorized representatives of the United States and the authorized representatives of the Government of India, in the following sectors: A.

The Government of India further agrees in cooperation with the Government of the United States, to coordinate the use of grant and loan funds provided for in paragraphs 1 ( B ) and 1 ( C ) of Article 2, with such direct dollar assistance as may be made available by the Government of the United States of America, so that both sources of financing may be channeled to specific and clearly identifiable economic development programs and projects.

With regard to the rupees accruing to uses indicated under Article 2, of the Agreement, the understanding of the Government of the United States of America, with respect to both paragraphs 1 ( B ) and 1 ( C ) of Article 2, is as follows: ( 1 )

Local currency will be advanced or reimbursed to the Government of India for financing agreed projects under paragraphs 1 ( B ) and 1 ( C ) of Article 2, of the Agreement upon the presentation of such documentation as the United States may specify.